Optimization over state feedback policies for robust control with constraints

By Paul J. Goulart, Eric C. Kerrigan, Jan M. Maciejowski. at - Automatisierungstechnik, 2006

652 citations recorded by the source corpus.

This paper is concerned with the optimal control of linear discrete-time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input. It is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence. This implies that a broad class of constrained finite horizon robust and optimal control problems, where the optimization is over affine state feedback policies, can be solved in a computationally efficient fashion using convex optimization methods. This equivalence result is used to design a robust receding horizon control (RHC) state feedback policy such that the closed-loop system is input-to-state stable (ISS) and the constraints are satisfied for all time and all allowable disturbance sequences. The cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance-free state and input sequences. The value of the receding horizon control law can be calculated at each sample instant using a single, tractable and convex quadratic program (QP) if the disturbance set is polytopic, or a tractable second-order cone program (SOCP) if the disturbance set is given by a 2-norm bound.

Subfields: Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5d927c49d18823985382d92d366c7e35d3dff3bf

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Citations in the corpus

Predictive Control for Linear and Hybrid Systems (2017, methodology): “74) The following result has been proven in [130], the convexity property has also appeared in [194][Section 7.”
Safe and Secure Networked Control Systems under Denial-of-Service Attacks (2009, background): “Recent research has shown that for the optimal control problems involving state and input constraints, more general causal feedback controllers can guarantee a larger set of initial states for which the constrained optimal control problem admits a feasible solution [3, 10, 17, 14, 19].”
Model predictive control: Recent developments and future promise (2014, background): “It was shown in Goulart et al. (2006) that there is a one-to-one nonlinear mapping”
Stochastic Model Predictive Control: An Overview and Perspectives for Future Research (2016, positive): “Inspired by [16], [74], and [75], an SMPC approach is presented in [47] for linear systems with Gaussian additive disturbances [see (7a)], where the feedback control law ( ) i $ r is defined in terms of an affine function of past disturbances”
Theory and Applications of Robust Optimization (2010, background): “me uncertainty (i.e., an ambiguous distribution). 5.Numerous other applications have been considered, including portfolio management [46, 129], coordination in wireless networks [135], robust control [84], and model adaptive control. Additional work in ane adaptability has been done in [57], where t”
Chance-Constrained Model Predictive Control for Drinking Water Networks (2014, methodology): “The approach relying on a purely deterministic unknown-butbounded description of the uncertainty has prevailed in the robust control literature, see [15–19], but the main disadvantage of the related strategies is the conservatism of the resultant control policy that negatively affects the utility fu”
Energy efficient building climate control using Stochastic Model Predictive Control and weather predictions (2010, methodology): “For approximating the dynamic programming problem we employ affine disturbance feedback, which has shown good performance in robust MPC problems [1], [2].”
Selected topics in robust convex optimization (2007, background): “A simple and fundamental fact proved in [19] (and independently, for the special case when yt ≡ xt, in [41]) is that (47), (42) are equivalent representations of non-anticipating affine control laws: for every controller of the form (41), there exists controller (42) which results in exactly the sam”
Safely Learning to Control the Constrained Linear Quadratic Regulator (2018, methodology): “We remark that similar observations have been used for constrained state feedback control in the finite horizon setting [11].”