Model predictive control based on linear programming - the explicit solution

By Alberto Bemporad, Francesco Borrelli, Manfred Morari. IEEE Transactions on Automatic Control, 2002

786 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/b5e680f19b5b36fdcf14aa636a0d5813a345eb0f

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Citations in the corpus

Fast Real-Time Constrained Predictive Current Control in Permanent Magnet Synchronous Machine-Based Automotive Traction Drives (2015, methodology): “Therefore, the solution of the Problem 3 can be obtained as a function of parameters θ via multiparametric linear programming (mp-LP) as it was shown in [30].”
Barrier Lyapunov functions for the output tracking control of constrained nonlinear switched systems (2013, background): “Model Predictive Control that represents an effective control design methodology for handling both constraints and performance issues has been investigated in [9,10].”
Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation (2009, methodology): “In the extreme case, this leads to an explict precomputation of the NMPC control law that has raised much interest in the linear MPC community [1], or a solution of the Hamilton-Jacobi-Bellman Equation, both of which are prohibitive for state and parameter dimensions above ten.”
Technical communique: On the facet-to-facet property of solutions to convex parametric quadratic programs (2006, methodology): “4 A new exploration strategy The algorithm in Bemporad et al. (2002b) does not rely on the facet-to-facet property but, as mentioned in the introduction, introduces a number of artificial cuts in the parameter space as it searches for the solution.”
Explicit Model-Predictive Control of a PWM Inverter With an LCL Filter (2009, methodology): “In explicit MPC (EMPC), this discrete-time optimal control problem is reformulated as a multiparametric program, as described in [ 19 ] and [20].”
Min-max control of constrained uncertain discrete-time linear systems (2003, methodology): “In all cases, the closed-loop system is simulated from the initial state with two different disturbances profiles shown in Fig. 2. 1) Nominal Case: We ignore the disturbance , and solve the resulting multiparametric linear program by using the approach of [ 12 ].”
An algorithm for multi-parametric quadratic programming and explicit MPC solutions (2001, methodology): “Choose the initial active set A0 as in [8], Prop.”
Integrator Backstepping using Barrier Functions for Systems with Multiple State Constraints (2005, methodology): “Key approaches include override control [3], set invariance and admissible set control [4], [5], the reference governor approach [6], and Linear Model Predictive Control [7].”
Constrained Optimal Control of Linear and Hybrid Systems (2003, methodology): “The computation effort can be moved offline by solving multiparametric programs, where the command inputs are the optimization variables and the measurements are the parameters [18].”
Nonlinear offset-free model predictive control (2012, methodology): “Methods have been developed [3,10,11,17] to solve (15), (16) explicitly to obtain a state feedback control law u(t) = c0(x̂(t), d̂(t), r(t)) in the form of a look-up table.”
Robust constrained model predictive control (2005, methodology): “Alternatively, parametric programming ideas could be applied to this problem [59].”
Stabilization with guaranteed safety using Control Lyapunov-Barrier Function (2016, methodology): “For example, Model Predictive Controlbased approach has been proposed in Bemporad, Borelli, and Morari (2002), Maciejowski (2002), Morari and Lee (1999) and ✩ The work of M.Z. Romdlony is supported by the Indonesian DIKTI scholarship program and the work of B. Jayawardhana is supported by the EU…”
A survey on explicit model predictive control (2009, background): “where the superscript i in (10) denotes the ith row, problem (3) can be mapped into the linear program (LP) [12]”
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).”
Geometric Algorithm for Multiparametric Linear Programming (2003, methodology): “Step 5. If there is primal degeneracy, then let U, P, D be the matrices in (12) after a Gauss reduction to (9a); determine x*(θ) from ( 13 ) and CRA(θ 0) from (14); choose y* among one of the possible optimizers.”
Linear offset-free Model Predictive Control (2009, methodology): “Methods have been developed [3,10,11,17] to solve (15), (16) explicitly to obtain a state feedback control law u(t) = c0(x̂(t), d̂(t), r(t)) in the form of a look-up table.”
Stochastic Model Predictive Control: An Overview and Perspectives for Future Research (2016, positive): “However, explicit MPC is not typically intended to replace standard MPC but, rather, to extend its area of application [4]–[6].”