The explicit linear quadratic regulator for constrained systems

By Alberto Bemporad, Manfred Morari, V. Dua, E. Pistikopoulos. 2003

3,448 citations recorded by the source corpus.

Subfields: Biochemistry, Control and Systems Engineering, Molecular Biology

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Citations in the corpus

Benchmarking Model-Based Reinforcement Learning (2019, methodology): “The algorithm uses a quadratic approximation on the RL reward function and a linear approximation on the dynamics, converting the problem solvable by linearquadratic regulator (LQR) [3].”
Optimal constrained control allocation in marine surface vessels with rudders (2003, methodology): “The optimization approach is based on solving several multi-parametric quadratic programs (mpQP) which allows explicit piecewise linear representations of the solution to be pre-computed (Bemporad et al. 2002, Tøndel et al. 2003a).”
Performance bounds for linear stochastic control (2009, methodology): “An even more sophisticated feedback control function is given by certainty-equivalent model predictive control (MPC) [16,21,10,15, 4,19], in which φ(z) is found by solving the optimization problem minimize Vmpc(x̃(T )) + T−1∑ τ=0 ( "x(x̃(τ )) + "u(v(τ )) ) subject to x̃(τ + 1) = Ax̃(τ ) + Bv(τ ), τ ”
Efficient interior point methods for multistage problems arising in receding horizon control (2012, methodology): “For certain problem formulations and small dimensions, multi-parametric programming can be used to calculate the optimal state-to-input map offline, enabling model predictive control of extremely highspeed systems [9], [10].”
Multi-Parametric Toolbox (MPT) (2004, methodology): “The cost (10a) may be linear (e.g., � ∈{ 1, ∞}) [4] or quadratic (e.g., � = 2) [ 8 ] whereby the matrices Q, R and Qf represent user-defined weights on the states and inputs.”
MPC-Based Approach to Active Steering for Autonomous Vehicle Systems (2005, methodology): “…phase, if the solution of a MILP or MIQP is prohibitive, the explicit piecewise affine form of the MPC law can be computed off line by using the multiparametric mixed integer programming (mp-MILP or mp-MIQP) solvers (Dua and Pistikopoulos, 2000; Bemporad et al., 2002; Borrelli et al., 2005a).”
Minimax approaches to robust model predictive control (2003, background): “It has recently been shown that nominal MPC controllers can be written explicitly as piecewise affine feedback laws (Bemporad et al., 2002a; Bemporad et al., 2002b).”
Parametric optimization and optimal control using algebraic geometry methods (2006, methodology): “This segmentation of the parameter space into regions is in analogy with the polytopic region partition that occurs in the linear off-line MPC case (Bemporad et al. 2002).”
Computational Complexity Certification for Real-Time MPC With Input Constraints Based on the Fast Gradient Method (2012, background): “The explicit solution is a piecewise affine map over a polyhedral partition of the state-space and can be stored efficiently such that fast online look-up is ensured [9], [12].”
Finite constraint set receding horizon quadratic control (2004, methodology): “Remark 11 (Terminal constraint set) Positively invariant sets can also be used directly in the formulation of receding horizon control schemes, see References [19, 39].”
Learning an Approximate Model Predictive Controller With Guarantees (2018, methodology): “For linear systems, the MPC optimization problem can be formulated as a multi-parametric quadratic program, which can be solved offline to obtain an explicit control law [2].”
Nonlinear offset-free model predictive control (2012, background): “In fact, the unconstrained MPC controlled KMPC in (23) is piecewise linear around the origin [6].”
Constrained Optimal Control of Linear and Hybrid Systems (2003, methodology): “The first method for solving multiparametric quadratic programs was proposed by Bemporad and coauthors in [25].”
Vehicle Yaw Stability Control by Coordinated Active Front Steering and Differential Braking in the Tire Sideslip Angles Domain (2013, background): “However, the recent development of multiparametric programming [16], which allows the optimal control problem to be solved offline, and of MPC for hybrid systems [hybrid MPC (hMPC)] [17], [18] have considerably increased the domain of applicability.”
A survey on explicit model predictive control (2009, methodology): “In [18] the authors suggest two ways to handle primal degeneracy.”