We consider the problem of discounted optimal state-feedback regulation for general unknown deterministic discrete-time systems. It is well known that open-loop instability of systems, non-quadratic cost functions and complex nonlinear dynamics, as well as the on-policy behavior of many reinforcement learning (RL) algorithms, make the design of model-free optimal adaptive controllers a challenging task. We depart from commonly used least-squares and neural network approximation methods in conventional model-free control theory, and propose a novel family of data-driven optimization algorithms based on linear programming, off-policy Q-learning and randomized experience replay. We develop both policy iteration (PI) and value iteration (VI) methods to compute an approximate optimal feedback controller with high precision and without the knowledge of a system model and stage cost function. Simulation studies confirm the effectiveness of the proposed methods.
We study the problem of optimal state-feedback tracking control for unknown discrete-time deterministic systems with input constraints. To handle input constraints, state-of-art methods utilize a certain nonquadratic stage cost function, which is sometimes limiting real systems. Furthermore, it is well known that Policy Iteration (PI) and Value Iteration (VI), two widely used algorithms in data-driven control, offer complementary strengths and weaknesses. In this work, a two-step transformation is employed, which converts the constrained-input optimal tracking problem to an unconstrained augme…
Multi-Step Optimal Tracking Control of Unknown Nonzero-Sum Games based on Least Squares and Linear Programming: An Application to a Fully-Automated, Dual-Hormone Artificial Pancreas
The aim of this paper is to propose a new data-driven control scheme for multi-input-multi-output linear time-invariant systems whose system model are completely unknown. Using a non-minimal input-output realization, the proposed method can be applied to the case where the system order is unknown, provided that its upper bound is known. A workaround against measurement noise is proposed and it is shown through simulation study that the proposed method is superior to the conventional methods when dealing with input/output data corrupted by measurement noise.
From Dissipativity Property to Data-Driven GAS Certificate of Degree-One Homogeneous Networks with Unknown Topology
School of Computing, Newcastle University（纽卡斯尔大学计算机学院）；Department of Electrical and Electronic Engineering, Imperial College London（帝国理工学院电气与电子工程系）；Department of Information Engineering, University of Florence（佛罗伦萨大学信息工程系）
The goal of this paper is to develop data-driven control design and evaluation strategies based on linear matrix inequalities (LMIs) and dynamic programming. We consider deterministic discrete-time LTI systems, where the system model is unknown. We propose efficient data collection schemes from the state-input trajectories together with data-driven LMIs to design state-feedback controllers for stabilization and linear quadratic regulation (LQR) problem. In addition, we investigate theoretically guaranteed exploration schemes to acquire valid data from the trajectories under different scenarios…
Dual control explicitly addresses the problem of trading off active exploration and exploitation in the optimal control of partially unknown systems. While the problem can be cast in the framework of stochastic dynamic programming, exact solutions are only tractable for discrete state and action spaces of very small dimension due to a series of nested minimization and expectation operations. We propose an approximate dual control method for systems with continuous state and input domain based on a rollout dynamic programming approach, splitting the control horizon into a dual and an exploitati…
Beijing Institute of Technology（北京理工大学）；Arizona State University（亚利桑那州立大学）
In this paper time-driven learning refers to the machine learning method that updates parameters in a prediction model continuously as new data arrives. Among existing approximate dynamic programming (ADP) and reinforcement learning (RL) algorithms, the direct heuristic dynamic programming (dHDP) has been shown an effective tool as demonstrated in solving several complex learning control problems. It continuously updates the control policy and the critic as system states continuously evolve. It is therefore desirable to prevent the time-driven dHDP from updating due to insignificant system eve…
In this paper, we consider the data-driven model invalidation problem for Lipschitz continuous systems, where instead of given mathematical models, only prior noisy sampled data of the systems are available. We show that this data-driven model invalidation problem can be solved using a tractable feasibility check. Our proposed approach consists of two main components: (i) a data-driven abstraction part that uses the noisy sampled data to over-approximate the unknown Lipschitz continuous dynamics with upper and lower functions, and (ii) an optimization-based model invalidation component that de…
Unknown-input observers (UIOs) allow for estimation of the states of an LTI system without knowledge of all inputs. In this paper, we provide a novel data-driven UIO based on behavioral system theory and the result known as Fundamental Lemma proposed by Jan Willems and coworkers. We give necessary and sufficient conditions on the data collected from the system for the existence of a UIO providing asymptotically converging state estimates, and propose a purely data-driven algorithm for their computation. Even though we focus on UIOs, our results also apply to the standard case of completely kno…
In this letter, we discuss the problem of optimal control for affine systems in the context of data-driven linear programming. First, we introduce a unified framework for the fixed point characterization of the value function, Q-function and relaxed Bellman operators. Then, in a model-free setting, we show how to synthesize and estimate Bellman inequalities from a small but sufficiently rich dataset. To guarantee exploration richness, we complete the extension of Willem's fundamental lemma to affine systems.
This paper presents a linear-programming based algorithm to perform data-driven stabilizing control of linear positive systems. A set of state-input-transition observations is collected up to magnitude-bounded noise. A state feedback controller and dual linear copositive Lyapunov function are created such that the set of all data-consistent plants is contained within the set of all stabilized systems. This containment is certified through the use of the Extended Farkas Lemma and solved via Linear Programming. Sign patterns and sparsity structure for the controller may be imposed using linear c…
In a direct data-driven approach, this paper studies the {\em property identification(ID)} problem to analyze whether an unknown linear system has a property of interest, e.g., stabilizability and structural properties. In sharp contrast to the model-based analysis, we approach it by directly using the input and state feedback data of the unknown system. Via a new concept of sufficient richness of input sectional data, we first establish the necessary and sufficient condition for the minimum input design to excite the system for property ID. Specifically, the input sectional data is sufficient…
In this work, we propose a data-driven approach for the construction of finite abstractions (a.k.a., symbolic models) for discrete-time deterministic control systems with unknown dynamics. We leverage notions of so-called alternating bisimulation functions (ABF), as a relation between each unknown system and its symbolic model, to quantify the mismatch between state behaviors of two systems. Accordingly, one can employ our proposed results to perform formal verification and synthesis over symbolic models and then carry the results back over unknown original systems. In our data-driven setting,…
This paper investigates the data-driven predictive control problems for a class of continuous-time industrial processes with completely unknown dynamics. The proposed approach employs the data-driven technique to get the system matrices online, using input-output measurements. Then, a model-free predictive control approach is designed to implement the receding-horizon optimization and realize the reference tracking. Feasibility of the proposed algorithm and stability of the closed-loop control systems are analyzed, respectively. Finally, a simulation example is provided to demonstrate the effe…
In this paper, a novel adaptive optimal control strategy is proposed to achieve the cooperative optimal output regulation of continuous-time linear multi-agent systems based on adaptive dynamic programming (ADP). The proposed method is different from those in the existing literature of ADP and cooperative output regulation in the sense that the knowledge of the exosystem dynamics is not required in the design of the exostate observers for those agents with no direct access to the exosystem. Moreover, an optimal control policy is obtained without the prior knowledge of the modeling information …
This paper studies the finite-horizon linear quadratic regulation problem where the dynamics of the system are assumed to be unknown and the state is accessible. Information on the system is given by a finite set of input-state data, where the input injected in the system is persistently exciting of a sufficiently high order. Using data, the optimal control law is then obtained as the solution of a suitable semidefinite program. The effectiveness of the approach is illustrated via numerical examples.
We propose a hierarchical learning architecture for predictive control in unknown environments. We consider a constrained nonlinear dynamical system and assume the availability of state-input trajectories solving control tasks in different environments. A parameterized environment model generates state constraints specific to each task, which are satisfied by the stored trajectories. Our goal is to find a feasible trajectory for a new task in an unknown environment. From stored data, we learn strategies in the form of target sets in a reduced-order state space. These strategies are applied to …
In this paper, we propose a data-driven approach to formally verify the safety of (potentially) unknown discrete-time continuous-space stochastic systems. The proposed framework is based on a notion of barrier certificates together with data collected from trajectories of unknown systems. We first reformulate the barrier-based safety verification as a robust convex problem (RCP). Solving the acquired RCP is hard in general because not only the state of the system lives in a continuous set, but also and more problematic, the unknown model appears in one of the constraints of RCP. Instead, we le…
Estimating the region of attraction for partially unknown nonlinear systems is a challenging issue. In this paper, we propose a tractable method to generate an estimated region of attraction with probability bounds, by searching an optimal polynomial barrier function. Chebyshev interpolants, Gaussian processes and sum-of-squares programmings are used in this paper. To approximate the unknown non-polynomial dynamics, a polynomial mean function of Gaussian processes model is computed to represent the exact dynamics based on the Chebyshev interpolants. Furthermore, probabilistic conditions are gi…
In this paper, we provide a direct data-driven approach to synthesize safety controllers for unknown linear systems affected by unknown-but-bounded disturbances, in which identifying the unknown model is not required. First, we propose a notion of $γ$-robust safety invariant ($γ$-RSI) sets and their associated state-feedback controllers, which can be applied to enforce invariance properties. Then, we formulate a data-driven computation of these sets in terms of convex optimization problems with linear matrix inequalities (LMI) as constraints, which can be solved based on a finite number of dat…
This work considers the optimal covariance steering problem for systems subject to both additive noise and uncertain parameters which may enter multiplicatively with the state and the control. The unknown parameters are modeled as a constant random variable sampled from a distribution with known moments. The optimal covariance steering problem is formulated using a moment-based representation of the system dynamics, which includes dependence between the unknown parameters and future states, and is solved using sequential convex programming. The proposed approach is demonstrated numerically usi…
Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven instability of reaction-diffusion-advection systems requires checking the Jacobian eigenvalues of infinitely many Fourier modes, which is computationally intractable. To overcome this limitation, this paper proposes mathematical optimization algorithms that determine the stability/instability of reaction-diffusion-advection systems by finite steps of algebr…
In this paper we propose a data-driven model for the spread of SARS-CoV-2 and use it to design optimal control strategies of human-mobility restrictions that both curb the epidemic and minimize the economic costs associated with implementing non-pharmaceutical interventions. We develop an extension of the SEIR epidemic model that captures the effects of changes in human mobility on the spread of the disease. The parameters of our data-driven model are learned using a multitask learning approach that leverages both data on the number of deaths across a set of regions, and cellphone data on indi…
Control using quantized feedback is a fundamental approach to system synthesis with limited communication capacity. In this paper, we address the stabilization problem for unknown linear systems with logarithmically quantized feedback, via a direct data-driven control method. By leveraging a recently developed matrix S-lemma, we prove a sufficient and necessary condition for the existence of a common stabilizing controller for all possible dynamics consistent with data, in the form of a linear matrix inequality. Moreover, we formulate semi-definite programming to solve the coarsest quantizatio…
Motivated by the goal of learning controllers for complex systems whose dynamics change over time, we consider the problem of designing control laws for systems that switch among a finite set of unknown discrete-time linear subsystems under unknown switching signals. To this end, we propose a method that uses data to directly design a control mechanism without any explicit identification step. Our approach is online, meaning that the data are collected over time while the system is evolving in closed-loop, and are directly used to iteratively update the controller. A major benefit of the propo…
This paper focuses on solving a data-driven distributionally robust optimization problem over a network of agents. The agents aim to minimize the worst-case expected cost computed over a Wasserstein ambiguity set that is centered at the empirical distribution. The samples of the uncertainty are distributed across the agents. Our approach consists of reformulating the problem as a semi-infinite program and then designing a distributed algorithm that solves a generic semi-infinite problem that has the same information structure as the reformulated problem. In particular, the decision variables c…
We study the problem of data-driven, constrained control of unknown nonlinear dynamics from a single ongoing and finite-horizon trajectory. We consider a one-step optimal control problem with a smooth, black-box objective, typically a composition of a known cost function and the unknown dynamics. We investigate an on-the-fly control paradigm, i.e., at each time step, the evolution of the dynamics and the first-order information of the cost are provided only for the executed control action. We propose an optimization-based control algorithm that iteratively minimizes a data-driven surrogate fun…
This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. Despite the centrality of this problem, most of the available methods critically rely on a precise knowledge of the system dynamics (thus requiring off-line system identification and model refinement). To this aim, in this paper we first show that the steady-state transfer function of a linear system can be computed directly from control experiments, bypassing explicit model identification. Then, we leverage the estimated …
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Cornerstone Robotics Limited（基石机器人有限公司）；The Chinese University of Hong Kong（香港中文大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
This paper addresses the problem of controlling a continuum manipulator (CM) in free or obstructed environments with no prior knowledge about the deformation behavior of the CM and the stiffness and geometry of the interacting obstructed environment. We propose a versatile data-driven priori-model-independent (PMI) control framework, in which various control paradigms (e.g. CM's position or shape control) can be defined based on the provided feedback. This optimal iterative algorithm learns the deformation behavior of the CM in interaction with an unknown environment, in real time, and then ac…
