Robust model predictive control of constrained linear systems with bounded disturbances

By David Q. Mayne, M. Seron, Sasa V. Rakovic. at - Automatisierungstechnik, 2005

1,693 citations recorded by the source corpus.

This paper provides a novel solution to the problem of robust model predictive control of constrained, linear, discrete-time systems in the presence of bounded disturbances. The optimal control problem that is solved online includes, uniquely, the initial state of the model employed in the problem as a decision variable. The associated value function is zero in a disturbance invariant set that serves as the 'origin' when bounded disturbances are present, and permits a strong stability result, namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances, to be obtained. The resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control.

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Citations in the corpus

Learning deep control policies for autonomous aerial vehicles with MPC-guided policy search (2015, methodology): “Model predictive control (MPC) is an effective and reliable method for controlling robotic systems, particularly autonomous aerial vehicles such as quadcopters, because of its robustness to moderate model errors [26], ability to use high-level objectives [41], and relative simplicity.”
Robust model predictive control: advantages and disadvantages of tube-based methods ⋆ (2011, background): “A further possibility is modification of the nominal optimal control problem P̄N (z;xe) to permit minimization with respect to (z,v) subject to the additional constraint x ∈ z + SK on z; see Mayne et al. (2005).”
Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning (2021, methodology): “robust MPC (RMPC) is tube-based MPC (28), which uses a nominal prediction model f̄(xk,uk) in the MPC optimization and tightens the constraints to account for unmodeled dynamics.”
Safely Learning to Control the Constrained Linear Quadratic Regulator (2018, background): “It is a relevant baseline, since it optimizes for average case performance Jσ but ensures safety for the worst-case behavior, consistent with MPC literature [10], [23].”
TUBE-BASED ROBUST NONLINEAR MODEL PREDICTIVE CONTROL1 (2007, unknown): “We use, as before (Mayne et al., 2005), a nominal controller Preprints of the 7th IFAC Symposium on Nonlinear Control Systems 21-24 August, 2007, Pretoria, South Africa”
Optimization over state feedback policies for robust control with constraints (2006, background): “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 ui = Kxi + ci, where K is computed off-line and on-line computation is limited to finding an admissible perturbation sequence {”
Robust output feedback model predictive control of constrained linear systems (2006, background): “(12) Since (AL) < 1, there exists a C set S̃ that is finite time computable and robust positively invariant (Raković, Kerrigan, Kouramas, & Mayne, 2005; Raković, 2005) for the system (11) and constraint set (Rn, ̃).”
Distributed model predictive control: A tutorial review and future research directions (2013, unknown): “3, we now synthetically describe the method recently proposed in [46] relying on the “tube-based” approach developed in [98] for the design of robust MPC.”
Learning an Approximate Model Predictive Controller With Guarantees (2018, methodology): “In [24] an additional error feedback is used to keep the real system state in a tube around the nominal system state for the system dynamics without disturbance.”
Model predictive control: Recent developments and future promise (2014, methodology): “If the system x+ = f (x, u, w) = Ax + Bu + w is linear, as considered in Chisci et al. (2001), Mayne and Langson (2001) and Mayne et al. (2005) then, employing the control parametrization u = Kx+v, first proposed inRossiter, Kouvaritakis, andRice (1998), yields x+ = AK x + Bv + w, AK , A + BK .”
PLATO: Policy learning using adaptive trajectory optimization (2016, background): “achieve considerable robustness to unexpected perturbations and model errors [18], making it an excellent choice for sample-efficient learning.”
Architectures for distributed and hierarchical Model Predictive Control - A review (2009, methodology): “An extension of this approach based on recent results on robust MPC design (see [63]) is reported in [104].”
A Review of Safe Reinforcement Learning: Methods, Theory and Applications (2022, background): “control [17, 132, 139, 183, 204, 231, 258], adaptive control [89, 115, 199, 238], robust control [26, 73, 112, 282], lyapunov function [56, 57] for RL stability and safety.”