Robust model predictive control of constrained linear systems with bounded disturbances

Mayne, D. Q.; Serón, María M.; Raković, Sas̆a V.

doi:10.1016/j.automatica.2004.08.019

Cited by 1,327 publications

(1,024 citation statements)

References 19 publications

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“…Remark 2 Note that the state feedback policy (4) subsumes the well-known class of "pre-stabilizing" control policies [1,6,19,25], in which the control policy takes the form u i = Kx i + c i , where K is computed off-line and on-line computation is limited to finding an admissible perturbation sequence {c i } N −1 i=0 .…”

Section: State Feedback Parameterizationmentioning

confidence: 99%

“…Finally, we add the following assumption, which allows V * N (·) in (25) to be used as an ISS-Lyapunov function:…”

Section: Input-to-state Stability (Iss) For Rhcmentioning

confidence: 99%

“…Hence, a popular approach in the predictive control literature is to compute one or more stabilizing linear state feedback control laws off-line and restrict the on-line computation to the selection of one of these control laws, followed by the computation of a finite sequence of admissible perturbations to the selected control law [1,6,19,25]. Though this approach considerably reduces the computational complexity, it is not always obvious how to best choose the linear control laws off-line so as to minimize conservativeness.…”

Section: Introductionmentioning

confidence: 99%

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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: State Feedback Parameterizationmentioning

confidence: 99%

“…Finally, we add the following assumption, which allows V * N (·) in (25) to be used as an ISS-Lyapunov function:…”

Section: Input-to-state Stability (Iss) For Rhcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization over state feedback policies for robust control with constraints

2006

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“…[1,2]) and yet surprisingly received very little interest in the academic literature [3,10,11,15]. A likely reason for this is that researchers in predictive control have focussed on proofs of issues such as guarantees of stability [6,18] and feasibility, robust stability [4], parametric methods [7] and more recently robust feasibility in the presence of bounded disturbances [9]. It should be noted that PFC techniques are much simpler to code and implement than conventional predictive control methods [3,8,15] and thus PFC is best viewed as an alternative to PID or other low level control law where the cost per control law is necessarily small but nevertheless one may desire attributes such as systematic constraint handling.…”

Section: Introductionmentioning

confidence: 99%

Pole-placement Predictive Functional Control for over-damped systems with real poles

2016

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This paper gives new insight and design proposals for Predictive Functional Control (PFC) algorithms. Common practice and indeed a requirement of PFC is to select a coincidence horizon greater than one for high-order systems and for the link between the design parameters and the desired dynamic to be weak. Here the proposal is to use parallel first-order models to form an independent prediction model and show that with these it is possible both to use a coincidence horizon of one and moreover to obtain precisely the desired closed-loop dynamics. It is shown through analysis that the use of a coincidence horizon of one greatly simplifies coding, tuning, constraint handling and implementation. The paper derives the key results for highorder and non-minimum phase processes and also demonstrates the flexibility and potential industrial utility of the proposal.

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“…Also, while regions of invariance are approximated analytically and numerically, they are used only to evaluate the performance of the controller and not while constructing motion plans. Another approach that is closely related to ours is Model Predictive Control with Tubes [15]. The idea is to solve the optimal control problem online with guaranteed "tubes" that the trajectories stay in.…”

Section: Related Workmentioning

confidence: 99%

Robust Online Motion Planning with Regions of Finite Time Invariance

Majumdar

Tedrake

2013

Springer Tracts in Advanced Robotics

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In this paper we consider the problem of generating motion plans for a nonlinear dynamical system that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, disturbances, and/or errors in state estimation. Furthermore, we consider the case where these plans must be generated online, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Previous work on feedback motion planning for nonlinear systems was limited to offline planning due to the computational cost of safety verification. Here we take a trajectory library approach by designing controllers that stabilize the nominal trajectories in the library and precomputing regions of finite time invariance ("funnels") for the resulting closed loop system. We leverage sums-of-squares programming in order to efficiently compute funnels which take into account bounded disturbances and uncertainty. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances. We demonstrate our method on a simulation of a plane flying through a two dimensional forest of polygonal trees with parametric uncertainty and disturbances in the form of a bounded "cross-wind".

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Robust model predictive control of constrained linear systems with bounded disturbances

Cited by 1,327 publications

References 19 publications

Optimization over state feedback policies for robust control with constraints

Optimization over state feedback policies for robust control with constraints

Pole-placement Predictive Functional Control for over-damped systems with real poles

Robust Online Motion Planning with Regions of Finite Time Invariance

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