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Register a new userSeparating Controller Design from Closed-Loop Design: A New Perspective on System-Level Controller Synthesis
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We show that given a desired closed-loop response for a system, there exists an affine subspace of controllers that achieve this response. By leveraging the existence of this subspace, we are able to separate controller design from closed-loop design by first synthesizing the desired closed-loop response and then synthesizing a controller that achieves the desired response. This is a useful extension to the recently introduced System Level Synthesis framework, in which the controller and closed-loop response are jointly synthesized and we cannot enforce controller-specific constraints without subjecting the closed-loop map to the same constraints. We demonstrate the importance of separating controller design from closed-loop design with an example in which communication delay and locality constraints cause standard SLS to be infeasible. Using our new two-step procedure, we are able to synthesize a controller that obeys the constraints while only incurring a 3% increase in LQR cost compared to the optimal LQR controller.
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To further understand the underlying mechanism of various reinforcement learning (RL) algorithms and also to better use the optimization theory to make further progress in RL, many researchers begin to revisit the linear-quadratic regulator (LQR) problem, whose setting is simple and yet captures the characteristics of RL. Inspired by this, this work is concerned with the model-free design of stochastic LQR controller for linear systems subject to Gaussian noises, from the perspective of both RL and primal-dual optimization. From the RL perspective, we first develop a new model-free off-policy policy iteration (MF-OPPI) algorithm, in which the sampled data is repeatedly used for updating the policy to alleviate the data-hungry problem to some extent. We then provide a rigorous analysis for algorithm convergence by showing that the involved iterations are equivalent to the iterations in the classical policy iteration (PI) algorithm. From the perspective of optimization, we first reformulate the stochastic LQR problem at hand as a constrained non-convex optimization problem, which is shown to have strong duality. Then, to solve this non-convex optimization problem, we propose a model-based primal-dual (MB-PD) algorithm based on the properties of the resulting Karush-Kuhn-Tucker (KKT) conditions. We also give a model-free implementation for the MB-PD algorithm by solving a transformed dual feasibility condition. More importantly, we show that the dual and primal update steps in the MB-PD algorithm can be interpreted as the policy evaluation and policy improvement steps in the PI algorithm, respectively. Finally, we provide one simulation example to show the performance of the proposed algorithms.
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This paper studies the controller synthesis problem for Linear Temporal Logic (LTL) specifications using (constrained) zonotope techniques. To begin with, we implement (constrained) zonotope techniques to partition the state space and further to verify whether the LTL specification can be satisfied. Once the LTL specification can be satisfied, the next step is to design a controller to guarantee the satisfaction of the LTL specification for dynamic systems. Based on the verification of the LTL specification, an abstraction-based control design approach is proposed in this paper: a novel abstraction construction is developed first, then finite local abstract controllers are designed to achieve the LTL specification, and finally the designed abstract controllers are combined and refined as the controller for the original system. The proposed control design strategy is illustrated via a numerical example from autonomous robots.
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