Sufficiently informative functions and the minimax feedback control of uncertain dynamic systems

Bertsekas, Dimitri P.; Rhodes, I.

doi:10.1109/tac.1973.1100241

Cited by 89 publications

(52 citation statements)

References 10 publications

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“…The main aim is to provide results that allow for the efficient computation of an optimal and stabilizing state feedback control policy that ensures a given set of state and input constraints are satisfied for all time, despite the presence of the disturbances. This is a problem that has been studied for some time now in the optimal control literature [4] and a number of different solutions are available, most of which draw on results from set invariance theory [5], 1 optimal control [7] or predictive control [22,24].…”

Section: Introductionmentioning

confidence: 99%

Optimization over state feedback policies for robust control with constraints

2006

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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.

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Section: Introductionmentioning

confidence: 99%

Optimization over state feedback policies for robust control with constraints

2006

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“…those policies that satisfy, for all w ∈ W, the state and control constraints (3), and the terminal constraint…”

Section: Optimal Control Problemmentioning

confidence: 99%

Optimal control of constrained, piecewise affine systems with bounded disturbances

Kerrigan

Mayne

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

109

108

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Finite horizon optimal control of piecewise affine systems with a piecewise affine (1-norm or ∞-norm) stage cost and terminal cost is considered. Provided the respective constraint sets are given as the unions of polyhedra, it is shown that the partial value functions and partial optimal control laws are piecewise affine on a polyhedral cover of the set of states that can be steered, by an admissible control policy, to a terminal set of states in a finite number of steps. Existing results only consider the case of systems without disturbances, or systems with disturbances that are independent of the state and input. This paper extends these results to the case where the disturbance is dependent on the state and input.

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“…Because of its importance, the above problem and derivations of it have been studied for some time now, with a large body of literature that falls under the broad banner of "robust control" (see [7,53] for some seminal work on the subject). The field of linear robust control, which is mainly motivated by frequency-domain performance criteria [57] and does not explicitly consider time-domain constraints as in the above problem formulation, is considered to be mature and a number of excellent references are available on the subject [19,29,58].…”

Section: Robust and Predictive Controlmentioning

confidence: 99%

Efficient robust optimization for robust control with constraints

2007

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This paper proposes an efficient computational technique for the optimal control of linear discrete-time systems subject to bounded disturbances with mixed linear constraints on the states and inputs. The problem of computing an optimal state feedback control policy, given the current state, is non-convex. A recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program. While the reparameterized problem is theoretically tractable, the number of variables is quadratic in the number of stages or horizon length N and has no apparent exploitable structure, leading to computational time of O(N 6 ) per iteration of an interior-point method. We focus on the case when the disturbance set is ∞-norm bounded or the linear map of a hypercube, and the cost function involves the minimization of a quadratic cost. Here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem, that is, the policy optimization problem may be decomposed into a set of coupled finite horizon control problems. This decomposition can then be formulated as a highly structured quadratic program, solvable by primal-dual interior-point methods in which each iteration requires O(N 3 ) time. This cubic iteration time can be guaranteed using a Riccati-based block factorization technique, which is standard in discrete-time optimal control. Numerical results are presented, using a standard sparse primal-dual interior point solver, that illustrate the efficiency of this approach.

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Sufficiently informative functions and the minimax feedback control of uncertain dynamic systems

Cited by 89 publications

References 10 publications

Optimization over state feedback policies for robust control with constraints

Optimization over state feedback policies for robust control with constraints

Optimal control of constrained, piecewise affine systems with bounded disturbances

Efficient robust optimization for robust control with constraints

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