Today's fast linear algebra and numerical optimization tools have pushed the frontier of model predictive control (MPC) forward, to the efficient control of highly nonlinear and hybrid systems. The field of hybrid MPC has demonstrated that exact optimal control law can be computed, e.g., by mixed-integer programming (MIP) under piecewise-affine (PWA) system models. Despite the elegant theory, online solving hybrid MPC is still out of reach for many applications. We aim to speed up MIP by combining geometric insights from hybrid MPC, a simple-yet-effective learning algorithm, and MIP warm start techniques. Following a line of work in approximate explicit MPC, the proposed learning-control algorithm, LNMS, gains computational advantage over MIP at little cost and is straightforward for practitioners to implement.
In this paper we propose a new approach to complement reinforcement learning (RL) with model-based control (in particular, Model Predictive Control - MPC). We introduce an algorithm, the MPC augmented RL (MPRL) that combines RL and MPC in a novel way so that they can augment each other's strengths. We demonstrate the effectiveness of the MPRL by letting it play against the Atari game Pong. For this task, the results highlight how MPRL is able to outperform both RL and MPC when these are used individually.
Model predictive control allows to provide high performance and safety guarantees in the form of constraint satisfaction. These properties, however, can be satisfied only if the underlying model, used for prediction, of the controlled process is sufficiently accurate. One way to address this challenge is by data-driven and machine learning approaches, such as Gaussian processes, that allow to refine the model online during operation. We present a combination of an output feedback model predictive control scheme and a Gaussian process-based prediction model that is capable of efficient online learning. To this end, the concept of evolving Gaussian processes is combined with recursive posterior prediction updates. The presented approach guarantees recursive constraint satisfaction and input-to-state stability with respect to the model-plant mismatch. Simulation studies underline that the Gaussian process prediction model can be successfully and efficiently learned online. The resulting computational load is significantly reduced via the combination of the recursive update procedure and by limiting the number of training data points while maintaining good performance.
In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture that is sufficient to implement the optimal Model Predictive Control (MPC) strategy for an LTI system with quadratic cost. Specifically, we propose AReN, an algorithm to generate Assured ReLU Architectures. AReN takes as input an LTI system with quadratic cost specification, and outputs a ReLU NN architecture with the assurance that there exist network weights that exactly implement the associated MPC controller. AReN thus offers new insight into the design of ReLU NN architectures for the control of LTI systems: instead of training a heuristically chosen NN architecture on data -- or iterating over many architectures until a suitable one is found -- AReN can suggest an adequate NN architecture before training begins. While several previous works were inspired by the fact that both ReLU NN controllers and optimal MPC controller are both Continuous, Piecewise-Linear (CPWL) functions, exploiting this similarity to design NN architectures with correctness guarantees has remained elusive. AReN achieves this using two novel features. First, we reinterpret a recent result about the implementation of CPWL functions via ReLU NNs to show that a CPWL function may be implemented by a ReLU architecture that is determined by the number of distinct affine regions in the function. Second, we show that we can efficiently over-approximate the number of affine regions in the optimal MPC controller without solving the MPC problem exactly. Together, these results connect the MPC problem to a ReLU NN implementation without explicitly solving the MPC and directly translates this feature to a ReLU NN architecture that comes with the assurance that it can implement the MPC controller. We show through numerical results the effectiveness of AReN in designing an NN architecture.
This work presents an explicit-implicit procedure to compute a model predictive control (MPC) law with guarantees on recursive feasibility and asymptotic stability. The approach combines an offline-trained fully-connected neural network with an online primal active set solver. The neural network provides a control input initialization while the primal active set method ensures recursive feasibility and asymptotic stability. The neural network is trained with a primal-dual loss function, aiming to generate control sequences that are primal feasible and meet a desired level of suboptimality. Since the neural network alone does not guarantee constraint satisfaction, its output is used to warm start the primal active set method online. We demonstrate that this approach scales to large problems with thousands of optimization variables, which are challenging for current approaches. Our method achieves a 2x reduction in online inference time compared to the best method in a benchmark suite of different solver and initialization strategies.
Dynamic games are an effective paradigm for dealing with the control of multiple interacting actors. This paper introduces ALGAMES (Augmented Lagrangian GAME-theoretic Solver), a solver that handles trajectory optimization problems with multiple actors and general nonlinear state and input constraints. Its novelty resides in satisfying the first order optimality conditions with a quasi-Newton root-finding algorithm and rigorously enforcing constraints using an augmented Lagrangian formulation. We evaluate our solver in the context of autonomous driving on scenarios with a strong level of interactions between the vehicles. We assess the robustness of the solver using Monte Carlo simulations. It is able to reliably solve complex problems like ramp merging with three vehicles three times faster than a state-of-the-art DDP-based approach. A model predictive control (MPC) implementation of the algorithm demonstrates real-time performance on complex autonomous driving scenarios with an update frequency higher than 60 Hz.
Electric motors are used in many applications and their efficiency is strongly dependent on their control. Among others, PI approaches or model predictive control methods are well-known in the scientific literature and industrial practice. A novel approach is to use reinforcement learning (RL) to have an agent learn electric drive control from scratch merely by interacting with a suitable control environment. RL achieved remarkable results with super-human performance in many games (e.g. Atari classics or Go) and also becomes more popular in control tasks like cartpole or swinging pendulum benchmarks. In this work, the open-source Python package gym-electric-motor (GEM) is developed for ease of training of RL-agents for electric motor control. Furthermore, this package can be used to compare the trained agents with other state-of-the-art control approaches. It is based on the OpenAI Gym framework that provides a widely used interface for the evaluation of RL-agents. The initial package version covers different DC motor variants and the prevalent permanent magnet synchronous motor as well as different power electronic converters and a mechanical load model. Due to the modular setup of the proposed toolbox, additional motor, load, and power electronic devices can be easily extended in the future. Furthermore, different secondary effects like controller interlocking time or noise are considered. An intelligent controller example based on the deep deterministic policy gradient algorithm which controls a series DC motor is presented and compared to a cascaded PI-controller as a baseline for future research. Fellow researchers are encouraged to use the framework in their RL investigations or to contribute to the functional scope (e.g. further motor types) of the package.
It is a long-standing challenge to enable an intelligent agent to learn in one environment and generalize to an unseen environment without further data collection and finetuning. In this paper, we consider a zero shot generalization problem setup that complies with biological intelligent agents' learning and generalization processes. The agent is first presented with previous experiences in the training environment, along with task description in the form of trajectory-level sparse rewards. Later when it is placed in the new testing environment, it is asked to perform the task without any interaction with the testing environment. We find this setting natural for biological creatures and at the same time, challenging for previous methods. Behavior cloning, state-of-art RL along with other zero-shot learning methods perform poorly on this benchmark. Given a set of experiences in the training environment, our method learns a neural function that decomposes the sparse reward into particular regions in a contingency-aware observation as a per step reward. Based on such decomposed rewards, we further learn a dynamics model and use Model Predictive Control (MPC) to obtain a policy. Since the rewards are decomposed to finer-granularity observations, they are naturally generalizable to new environments that are composed of similar basic elements. We demonstrate our method on a wide range of environments, including a classic video game -- Super Mario Bros, as well as a robotic continuous control task. Please refer to the project page for more visualized results.
In this paper, we introduce an actor-critic algorithm called Deep Value Model Predictive Control (DMPC), which combines model-based trajectory optimization with value function estimation. The DMPC actor is a Model Predictive Control (MPC) optimizer with an objective function defined in terms of a value function estimated by the critic. We show that our MPC actor is an importance sampler, which minimizes an upper bound of the cross-entropy to the state distribution of the optimal sampling policy. In our experiments with a Ballbot system, we show that our algorithm can work with sparse and binary reward signals to efficiently solve obstacle avoidance and target reaching tasks. Compared to previous work, we show that including the value function in the running cost of the trajectory optimizer speeds up the convergence. We also discuss the necessary strategies to robustify the algorithm in practice.
We present an approach to learn an object-centric forward model, and show that this allows us to plan for sequences of actions to achieve distant desired goals. We propose to model a scene as a collection of objects, each with an explicit spatial location and implicit visual feature, and learn to model the effects of actions using random interaction data. Our model allows capturing the robot-object and object-object interactions, and leads to more sample-efficient and accurate predictions. We show that this learned model can be leveraged to search for action sequences that lead to desired goal configurations, and that in conjunction with a learned correction module, this allows for robust closed loop execution. We present experiments both in simulation and the real world, and show that our approach improves over alternate implicit or pixel-space forward models. Please see our project page (https://judyye.github.io/ocmpc/) for result videos.
Dexterous multi-fingered hands can provide robots with the ability to flexibly perform a wide range of manipulation skills. However, many of the more complex behaviors are also notoriously difficult to control: Performing in-hand object manipulation, executing finger gaits to move objects, and exhibiting precise fine motor skills such as writing, all require finely balancing contact forces, breaking and reestablishing contacts repeatedly, and maintaining control of unactuated objects. Learning-based techniques provide the appealing possibility of acquiring these skills directly from data, but current learning approaches either require large amounts of data and produce task-specific policies, or they have not yet been shown to scale up to more complex and realistic tasks requiring fine motor skills. In this work, we demonstrate that our method of online planning with deep dynamics models (PDDM) addresses both of these limitations; we show that improvements in learned dynamics models, together with improvements in online model-predictive control, can indeed enable efficient and effective learning of flexible contact-rich dexterous manipulation skills -- and that too, on a 24-DoF anthropomorphic hand in the real world, using just 4 hours of purely real-world data to learn to simultaneously coordinate multiple free-floating objects. Videos can be found at https://sites.google.com/view/pddm/
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems.
In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample applications (e.g., grasping tasks and human-robot collaborations) further show the applicability of imitation learning in a wide range of domains. While numerous literature is dedicated to the learning of human skills in unconstrained environment, the problem of learning constrained motor skills, however, has not received equal attention yet. In fact, constrained skills exist widely in robotic systems. For instance, when a robot is demanded to write letters on a board, its end-effector trajectory must comply with the plane constraint from the board. In this paper, we aim to tackle the problem of imitation learning with linear constraints. Specifically, we propose to exploit the probabilistic properties of multiple demonstrations, and subsequently incorporate them into a linearly constrained optimization problem, which finally leads to a non-parametric solution. In addition, a connection between our framework and the classical model predictive control is provided. Several examples including simulated writing and locomotion tasks are presented to show the effectiveness of our framework.
The Holy Grail of a decentralised stablecoin is achieved on rigorous mathematical frameworks, obtaining multiple advantageous proofs: stability, convergence, truthfulness, faithfulness, and malicious-security. These properties could only be attained by the novel and interdisciplinary combination of previously unrelated fields: model predictive control, deep learning, alternating direction method of multipliers (consensus-ADMM), mechanism design, secure multi-party computation, and zero-knowledge proofs. For the first time, this paper proves: - the feasibility of decentralising the central bank while securely preserving its independence in a decentralised computation setting - the benefits for price stability of combining mechanism design, provable security, and control theory, unlike the heuristics of previous stablecoins - the implementation of complex monetary policies on a stablecoin, equivalent to the ones used by central banks and beyond the current fixed rules of cryptocurrencies that hinder their price stability - methods to circumvent the impossibilities of Guaranteed Output Delivery (G.O.D.) and fairness: standing on truthfulness and faithfulness, we reach G.O.D. and fairness under the assumption of rational parties As a corollary, a decentralised artificial intelligence is able to conduct the monetary policy of a stablecoin, minimising human intervention.
Traditional planning and control methods could fail to find a feasible trajectory for an autonomous vehicle to execute amongst dense traffic on roads. This is because the obstacle-free volume in spacetime is very small in these scenarios for the vehicle to drive through. However, that does not mean the task is infeasible since human drivers are known to be able to drive amongst dense traffic by leveraging the cooperativeness of other drivers to open a gap. The traditional methods fail to take into account the fact that the actions taken by an agent affect the behaviour of other vehicles on the road. In this work, we rely on the ability of deep reinforcement learning to implicitly model such interactions and learn a continuous control policy over the action space of an autonomous vehicle. The application we consider requires our agent to negotiate and open a gap in the road in order to successfully merge or change lanes. Our policy learns to repeatedly probe into the target road lane while trying to find a safe spot to move in to. We compare against two model-predictive control-based algorithms and show that our policy outperforms them in simulation.
This paper presents a real-time lane change control framework of autonomous driving in dense traffic, which exploits cooperative behaviors of other drivers. This paper focuses on heavy traffic where vehicles cannot change lanes without cooperating with other drivers. In this case, classical robust controls may not apply since there is no safe area to merge to without interacting with the other drivers. That said, modeling complex and interactive human behaviors is highly non-trivial from the perspective of control engineers. We propose a mathematical control framework based on Model Predictive Control (MPC) encompassing a state-of-the-art Recurrent Neural network (RNN) architecture. In particular, RNN predicts interactive motions of other drivers in response to potential actions of the autonomous vehicle, which are then systematically evaluated in safety constraints. We also propose a real-time heuristic algorithm to find locally optimal control inputs. Finally, quantitative and qualitative analysis on simulation studies are presented to illustrate the benefits of the proposed framework.
This paper proposes a learning-based model predictive control (MPC) approach for the thermal control of a four-zone smart building. The objectives are to minimize energy consumption and maintain the residents' comfort. The proposed control scheme incorporates learning with the model-based control. The occupancy profile in the building zones are estimated in a long-term horizon through the artificial neural network (ANN), and this data is fed into the model-based predictor to get the indoor temperature predictions. The Energy Plus software is utilized as the actual dataset provider (weather data, indoor temperature, energy consumption). The optimization problem, including the actual and predicted data, is solved in each step of the simulation and the input setpoint temperature for the heating/cooling system, is generated. Comparing the results of the proposed approach with the conventional MPC results proved the significantly better performance of the proposed method in energy savings (40.56% less cooling power consumption and 16.73% less heating power consumption), and residents' comfort.
This paper introduces the autonomous system of the "Smart Shark II" which won the Formula Student Autonomous China (FSAC) Competition in 2018. In this competition, an autonomous racecar is required to complete autonomously two laps of unknown track. In this paper, the author presents the self-driving software structure of this racecar which ensure high vehicle speed and safety. The key components ensure a stable driving of the racecar, LiDAR-based and Vision-based cone detection provide a redundant perception; the EKF-based localization offers high accuracy and high frequency state estimation; perception results are accumulated in time and space by occupancy grid map. After getting the trajectory, a model predictive control algorithm is used to optimize in both longitudinal and lateral control of the racecar. Finally, the performance of an experiment based on real-world data is shown.
Model-based Reinforcement Learning (MBRL) allows data-efficient learning which is required in real world applications such as robotics. However, despite the impressive data-efficiency, MBRL does not achieve the final performance of state-of-the-art Model-free Reinforcement Learning (MFRL) methods. We leverage the strengths of both realms and propose an approach that obtains high performance with a small amount of data. In particular, we combine MFRL and Model Predictive Control (MPC). While MFRL's strength in exploration allows us to train a better forward dynamics model for MPC, MPC improves the performance of the MFRL policy by sampling-based planning. The experimental results in standard continuous control benchmarks show that our approach can achieve MFRL`s level of performance while being as data-efficient as MBRL.
Nonlinear model predictive control (NMPC) is one of the few control methods that can handle multivariable nonlinear controlsystems with constraints. Gaussian processes (GPs) present a powerful tool to identify the required plant model and quantifythe residual uncertainty of the plant-model mismatch. It is crucial to consider this uncertainty, since it may lead to worsecontrol performance and constraint violations. In this paper we propose a new method to design a GP-based NMPC algorithmfor finite horizon control problems. The method generates Monte Carlo samples of the GP offline for constraint tighteningusing back-offs. The tightened constraints then guarantee the satisfaction of chance constraints online. Advantages of our proposed approach over existing methods include fast online evaluation, consideration of closed-loop behaviour, and thepossibility to alleviate conservativeness by considering both online learning and state dependency of the uncertainty. The algorithm is verified on a challenging semi-batch bioprocess case study.