In this manuscript, decentralized robust interval type-2 fuzzy model predictive control for Takagi-Sugeno large-scale systems is studied. The mentioned large-scale system consists a number of interval type-2 (IT2) fuzzy Takagi-Sugeno (T-S) subsystems. An important matter and necessities that limit the practical application of model predictive control are the online computational cost and burden of the existence frameworks. For model predictive control of T-S fuzzy large-scale systems, the online computational burden is even worse and in some cases, they cannot be solved in an expected time. Especially for severe large-scale systems with disturbances, existing model predictive control of T-S fuzzy large-scale systems usually leads to a very conservative solution. So, researchers have many challenges and difficulties in finding a reasonable solution in a short time. Although, more relaxed results can be achieved by the proposed fuzzy model predictive control approach which adopts T-S large-scale systems with nonlinear subsystems, many restrictions are not considered in these approaches. In this paper, challenges are solved and the MPC is designed for a nonlinear IT2 fuzzy large-scale system with uncertainties and disturbances. Besides, online optimization problem is solved and results are proposed. Consequently, online computational cost of the optimization problem is reduced considerably. At the end, by two practical examples, the effectiveness of the proposed algorithm is illustrated.
In this paper, we propose a suboptimal moving horizon estimator for a general class of nonlinear systems. For the stability analysis, we transfer the "feasibility-implies-stability/robustness" paradigm from model predictive control to the context of moving horizon estimation in the following sense: Using a suitably defined, feasible candidate solution based on an auxiliary observer, robust stability of the proposed suboptimal estimator is inherited independently of the horizon length and even if no optimization is performed. Moreover, the proposed design allows for the choice between two cost functions different in structure: the former in the manner of a standard least squares approach, which is typically used in practice, and the latter following a time-discounted modification, resulting in better theoretical guarantees. We apply the proposed suboptimal estimator to a nonlinear chemical reactor process, verify the theoretical assumptions, and show that even a few iterations of the optimizer are sufficient to significantly improve the estimation results of the auxiliary observer. Furthermore, we illustrate the flexibility of the proposed design by employing different solvers and compare the performance with two state-of-the-art fast MHE schemes from the literature.
Buildings directly and indirectly emit a large share of current CO2 emissions. There is a high potential for CO2 savings through modern control methods in building automation systems (BAS) like model predictive control (MPC). For a proper control, MPC needs mathematical models to predict the future behavior of the controlled system. For this purpose, digital twins of the building can be used. However, with current methods in existing buildings, a digital twin set up is usually labor-intensive. Especially connecting the different components of the technical system to an overall digital twin of the building is time-consuming. Piping and instrument diagrams (P&ID) can provide the needed information, but it is necessary to extract the information and provide it in a standardized format to process it further. In this work, we present an approach to recognize symbols and connections of P&ID from buildings in a completely automated way. There are various standards for graphical representation of symbols in P&ID of building energy systems. Therefore, we use different data sources and standards to generate a holistic training data set. We apply algorithms for symbol recognition, line recognition and derivation of connections to the data sets. Furthermore, the result is exported to a format that provides semantics of building energy systems. The symbol recognition, line recognition and connection recognition show good results with an average precision of 93.7%, which can be used in further processes like control generation, (distributed) model predictive control or fault detection. Nevertheless, the approach needs further research.
Koopman operators are of infinite dimension and capture the characteristics of nonlinear dynamics in a lifted global linear manner. The finite data-driven approximation of Koopman operators results in a class of linear predictors, useful for formulating linear model predictive control (MPC) of nonlinear dynamical systems with reduced computational complexity. However, the robustness of the closed-loop Koopman MPC under modeling approximation errors and possible exogenous disturbances is still a crucial issue to be resolved. Aiming at the above problem, this paper presents a robust tube-based MPC solution with Koopman operators, i.e., r-KMPC, for nonlinear discrete-time dynamical systems with additive disturbances. The proposed controller is composed of a nominal MPC using a lifted Koopman model and an off-line nonlinear feedback policy. The proposed approach does not assume the convergence of the approximated Koopman operator, which allows using a Koopman model with a limited order for controller design. Fundamental properties, e.g., stabilizability, observability, of the Koopman model are derived under standard assumptions with which, the closed-loop robustness and nominal point-wise convergence are proven. Simulated examples are illustrated to verify the effectiveness of the proposed approach.
Autonomous driving at intersections is one of the most complicated and accident-prone traffic scenarios, especially with mixed traffic participants such as vehicles, bicycles and pedestrians. The driving policy should make safe decisions to handle the dynamic traffic conditions and meet the requirements of on-board computation. However, most of the current researches focuses on simplified intersections considering only the surrounding vehicles and idealized traffic lights. This paper improves the integrated decision and control framework and develops a learning-based algorithm to deal with complex intersections with mixed traffic flows, which can not only take account of realistic characteristics of traffic lights, but also learn a safe policy under different safety constraints. We first consider different velocity models for green and red lights in the training process and use a finite state machine to handle different modes of light transformation. Then we design different types of distance constraints for vehicles, traffic lights, pedestrians, bicycles respectively and formulize the constrained optimal control problems (OCPs) to be optimized. Finally, reinforcement learning (RL) with value and policy networks is adopted to solve the series of OCPs. In order to verify the safety and efficiency of the proposed method, we design a multi-lane intersection with the existence of large-scale mixed traffic participants and set practical traffic light phases. The simulation results indicate that the trained decision and control policy can well balance safety and tracking performance. Compared with model predictive control (MPC), the computational time is three orders of magnitude lower.
Control of non-condensing non-ideal-gas power cycles is challenging because their output power dynamics depend on complex system interactions, non-ideal-gas effects complicate turbomachinery behavior, and state constraints must be respected. This article presents a control methodology for these systems, comprising a control modeling approach and model predictive control (MPC) strategy. This methodology is demonstrated on the high-pressure side of a simple supercritical CO2 cycle power block, composed of a variable-speed compressor, heat exchanger, and fixed-speed turbine. The control model is developed by applying timescale-separation arguments to a high-fidelity simulation model and locally linearizing non-ideal-gas turbomachinery performance maps. MPC is implemented by linearizing the control model online at each sampling instant. Closed-loop simulations with a full-order gas-dynamics truth model demonstrate the effectiveness of the proposed control methodology. In response to load changes, the controller maintains high turbine inlet temperatures while achieving net power output ramp rates in excess of 100% of nameplate output per minute. The controller often acts at the intersection of motor torque, compressor surge, and turbine inlet temperature constraints, and performs well from 35 to 105% of nameplate capacity with no parameter scheduling. Good performance and fast update rates are obtained via online linearization. The results demonstrate the suitability of MPC for the supercritical CO2 cycle, and the proposed methodology is extensible to more complex cycle variants such as the recuperated and recompression cycle.
In this work, we have developed a framework for synthesizing data driven controllers for a class of uncertain switched systems arising in an application to physical activity interventions. In particular, we present an application of probabilistic model predictive control to design an efficient, tractable, and adaptive intervention using behavioral data sets i.e. physical activity behavior. The models of physical activity for each individual are provided for the design of controllers that maximize the probability of achieving a desired physical activity goal subject to intervention specifications. We have tailored the mixed-integer programming-based approach for evaluating the Model Predictive Control decision at each time step.
Abstract-In this manuscript, model predictive control for class of discrete fuzzy large-scale systems subjected to bounded time-varying delay and disturbances is studied. The considered method is Razumikhin for time-varying delay large-scale systems, in which it includes a Lyapunov function associated with the original non-augmented state space of system dynamics in comparison with the Krasovskii method. As a rule, the Razumikhin method has a perfect potential to avoid the inherent complexity of the Krasovskii method especially in the presence of large delays and disturbances. The considered large-scale system in this manuscript is decomposed into several subsystems, each of which is represented by a fuzzy Takagi-Sugeno (T-S) model and the interconnection between any two subsystems is considered. Because the main section of the model predictive control is optimization, the hierarchical scheme is performed for the optimization problem. Furthermore, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are studied. The linear matrix inequalities (LMIs) method is performed for our computations. So the closed-loop large-scale system is asymptotically stable. Ultimately, by two examples, the effectiveness of the proposed method is illustrated, and a comparison with other papers is made by remarks.
In this paper we aim to provide analysis and insights (often based on visualization), which explain the beneficial effects of on-line decision making on top of off-line training. In particular, through a unifying abstract mathematical framework, we show that the principal AlphaZero/TD-Gammon ideas of approximation in value space and rollout apply very broadly to deterministic and stochastic optimal control problems, involving both discrete and continuous search spaces. Moreover, these ideas can be effectively integrated with other important methodologies such as model predictive control, adaptive control, decentralized control, discrete and Bayesian optimization, neural network-based value and policy approximations, and heuristic algorithms for discrete optimization.
The fact that event-triggered control (ETC) often exhibits an improved performance-communication tradeoff over time-triggered control renders it especially useful for Networked Control Systems (NCSs). However, it has proven difficult to characterize the traffic produced by ETC a priori. Rollout ETC addresses this issue by using a triggering and control law that is implicitly defined by the solution to an optimal control problem (OCP), instead of an explicit one as in classical ETC. This allows to directly incorporate predefined constraints on the transmission traffic as well as on states and inputs. In this article, we examine the practically relevant case when output instead of state measurements are available, and measurements as well as the LTI plant are subject to uncertainties. To address these challenges, we adapt methods from robust tube-based model predictive control and propose three different strategies to implement an error feedback in an NCSs setup, the applicability of which depends on the capabilities of the actuator. We establish recursive feasibility, robust constraint satisfaction and convergence. Finally, we illustrate our results in a numerical example.
Model predictive control (MPC) is a method to formulate the optimal scheduling problem for grid flexibilities in a mathematical manner. The resulting time-constrained optimization problem can be re-solved in each optimization time step using classical optimization methods such as Second Order Cone Programming (SOCP) or Interior Point Methods (IPOPT). When applying MPC in a rolling horizon scheme, the impact of uncertainty in forecasts on the optimal schedule is reduced. While MPC methods promise accurate results for time-constrained grid optimization they are inherently limited by the calculation time needed for large and complex power system models. Learning the optimal control behaviour using function approximation offers the possibility to determine near-optimal control actions with short calculation time. A Neural Predictive Control (NPC) scheme is proposed to learn optimal control policies for linear and nonlinear power systems through imitation. It is demonstrated that this procedure can find near-optimal solutions, while reducing the calculation time by an order of magnitude. The learned controllers are validated using a benchmark smart grid.
This paper studies the value of communicated motion predictions in the longitudinal control of connected automated vehicles (CAVs). We focus on a safe cooperative adaptive cruise control (CACC) design and analyze the value of vehicle-to-vehicle (V2V) communication in the presence of uncertain front vehicle acceleration. The interest in CACC is motivated by the potential improvement in energy consumption and road throughput. In order to quantify this potential, we characterize experimentally the relationship between inter-vehicular gap, vehicle speed, and (reduction of) energy consumption for a compact plug-in hybrid electric vehicle. The resulting model is leveraged to show efficacy of our control design, which pursues small inter-vehicle gaps between consecutive CAVs and, therefore, improved energy efficiency. Our proposed control design is based on a robust model predictive control framework to systematically account for the system uncertainties. We present a set of thorough simulations aimed at quantifying energy efficiency improvement when vehicle states and predictions exchanged via V2V communication are used in the control law.
Horizon length and model accuracy are defining factors when designing a Model Predictive Controller. While long horizons and detailed models have a positive effect on control performance, computational complexity increases. As predictions become less precise over the horizon length, it is worth investigating a combination of different models and varying time step size. Here, we propose a Model Predictive Control scheme that splits the prediction horizon into two segments. A detailed model is used for the short-term prediction horizon and a simplified model with an increased sampling time is employed for the long-term horizon. This approach combines the advantage of a long prediction horizon with a reduction of computational effort due to a simplified model and less decision variables. The presented Model Predictive Control is recursively feasible. A simulation study demonstrates the effectiveness of the proposed method: employing a long prediction horizon with advantages regarding computational complexity.
Nonlinear model predictive control (NMPC) is an efficient approach for the control of nonlinear multivariable dynamic systems with constraints, which however requires an accurate plant model. Plant models can often be determined from first principles, parts of the model are however difficult to derive using physical laws alone. In this paper a hybrid Gaussian process (GP) first principles modeling scheme is proposed to overcome this issue, which exploits GPs to model the parts of the dynamic system that are difficult to describe using first principles. GPs not only give accurate predictions, but also quantify the residual uncertainty of this model. It is vital to account for this uncertainty in the control algorithm, to prevent constraint violations and performance deterioration. Monte Carlo samples of the GPs are generated offline to tighten constraints of the NMPC to ensure joint probabilistic constraint satisfaction online. Advantages of our method include fast online evaluation times, possibility to account for online learning alleviating conservativeness, and exploiting the flexibility of GPs and the data efficiency of first principle models. The algorithm is verified on a case study involving a challenging semi-batch bioreactor.
This paper presents a cooperative target defense strategy using nonlinear model-predictive control (NMPC) framework for a two--targets two--attackers (2T2A) game. The 2T2A game consists of two attackers and two targets. Each attacker needs to capture a designated target individually. However, the two targets cooperate to lure the attackers into a collision. We assume that the cooperative target pair do not have perfect knowledge of the attacker states, and hence they estimate the attacker states using an extended Kalman filter (EKF). The NMPC scheme computes closed- loop optimal control commands for the targets while respecting imposed state and control constraints. Theoretical analysis is carried out to determine regions that will lead to the targets' survival, given the initial positions of the attacker and target agents. Numerical simulations are carried out to evaluate the performance of the proposed NMPC- based strategy for different scenarios.
Connected and Automated Vehicles (CAVs), particularly those with a hybrid electric powertrain, have the potential to significantly improve vehicle energy savings in real-world driving conditions. In particular, the Eco-Driving problem seeks to design optimal speed and power usage profiles based on available information from connectivity and advanced mapping features to minimize the fuel consumption over an itinerary. This paper presents a hierarchical multi-layer Model Predictive Control (MPC) approach for improving the fuel economy of a 48V mild-hybrid powertrain in a connected vehicle environment. Approximate Dynamic Programming (ADP) is used to solve the Receding Horizon Optimal Control Problem (RHOCP), where the terminal cost for the RHOCP is approximated as the base-policy obtained from the long-term optimization. The controller was extensively tested virtually (using both deterministic and Monte Carlo simulations) across multiple real-world routes where energy savings of more than 20\% have been demonstrated. Further, the developed controller was deployed and tested at a proving ground in real-time on a test vehicle equipped with a rapid prototyping embedded controller. Real-time in-vehicle testing confirmed the energy savings observed in simulation and demonstrated the ability of the developed controller to be effective in real-time applications.
Space mission design places a premium on cost and operational efficiency. The search for new science and life beyond Earth calls for spacecraft that can deliver scientific payloads to geologically rich yet hazardous landing sites. At the same time, the last four decades of optimization research have put a suite of powerful optimization tools at the fingertips of the controls engineer. As we enter the new decade, optimization theory, algorithms, and software tooling have reached a critical mass to start seeing serious application in space vehicle guidance and control systems. This survey paper provides a detailed overview of recent advances, successes, and promising directions for optimization-based space vehicle control. The considered applications include planetary landing, rendezvous and proximity operations, small body landing, constrained attitude reorientation, endo-atmospheric flight including ascent and reentry, and orbit transfer and injection. The primary focus is on the last ten years of progress, which have seen a veritable rise in the number of applications using three core technologies: lossless convexification, sequential convex programming, and model predictive control. The reader will come away with a well-rounded understanding of the state-of-the-art in each space vehicle control application, and will be well positioned to tackle important current open problems using convex optimization as a core technology.
Networks are landmarks of many complex phenomena where interweaving interactions between different agents transform simple local rule-sets into nonlinear emergent behaviors. While some recent studies unveil associations between the network structure and the underlying dynamical process, identifying stochastic nonlinear dynamical processes continues to be an outstanding problem. Here we develop a simple data-driven framework based on operator-theoretic techniques to identify and control stochastic nonlinear dynamics taking place over large-scale networks. The proposed approach requires no prior knowledge of the network structure and identifies the underlying dynamics solely using a collection of two-step snapshots of the states. This data-driven system identification is achieved by using the Koopman operator to find a low dimensional representation of the dynamical patterns that evolve linearly. Further, we use the global linear Koopman model to solve critical control problems by applying to model predictive control (MPC)--typically, a challenging proposition when applied to large networks. We show that our proposed approach tackles this by converting the original nonlinear programming into a more tractable optimization problem that is both convex and with far fewer variables.
The cost of the power distribution infrastructures is driven by the peak power encountered in the system. Therefore, the distribution network operators consider billing consumers behind a common transformer in the function of their peak demand and leave it to the consumers to manage their collective costs. This management problem is, however, not trivial. In this paper, we consider a multi-agent residential smart grid system, where each agent has local renewable energy production and energy storage, and all agents are connected to a local transformer. The objective is to develop an optimal policy that minimizes the economic cost consisting of both the spot-market cost for each consumer and their collective peak-power cost. We propose to use a parametric Model Predictive Control (MPC)-scheme to approximate the optimal policy. The optimality of this policy is limited by its finite horizon and inaccurate forecasts of the local power production-consumption. A Deterministic Policy Gradient (DPG) method is deployed to adjust the MPC parameters and improve the policy. Our simulations show that the proposed MPC-based Reinforcement Learning (RL) method can effectively decrease the long-term economic cost for this smart grid problem.
We present an end-to-end online motion planning framework that uses a data-driven approach to navigate a heterogeneous robot team towards a global goal while avoiding obstacles in uncertain environments. First, we use stochastic model predictive control (SMPC) to calculate control inputs that satisfy robot dynamics, and consider uncertainty during obstacle avoidance with chance constraints. Second, recurrent neural networks are used to provide a quick estimate of future state uncertainty considered in the SMPC finite-time horizon solution, which are trained on uncertainty outputs of various simultaneous localization and mapping algorithms. When two or more robots are in communication range, these uncertainties are then updated using a distributed Kalman filtering approach. Lastly, a Deep Q-learning agent is employed to serve as a high-level path planner, providing the SMPC with target positions that move the robots towards a desired global goal. Our complete methods are demonstrated on a ground and aerial robot simultaneously (code available at: https://github.com/AlexS28/SABER).