Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations

By Jean B. Lasserre, Didier Henrion, Christophe Prieur, Emmanuel Trélat. SIAM Journal of Control and Optimization, 2007

322 citations recorded by the source corpus.

We consider the class of nonlinear optimal control problems (OCPs) with polynomial data, i.e., the differential equation, state and control constraints, and cost are all described by polynomials, and more generally for OCPs with smooth data. In addition, state constraints as well as state and/or action constraints are allowed. We provide a simple hierarchy of LMI- (linear matrix inequality)-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Under some convexity assumptions, the sequence converges to the optimal value of the OCP. Preliminary results show that good approximations are obtained with few moments.

Subfields: Computational Mechanics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c6377ca97522a68cd9634ac7887889fc897a0a20

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

Approximate dynamic programming via iterated Bellman inequalities (2015, background): “See [64, 65] for more on SOS, and [13, 66, 67] for other work on value function approximation with polynomial data.”
GloptiPoly 3: moments, optimization and semidefinite programming (2007, methodology): “For example, consider the GPM arising when solving polynomi al optimal control problems as detailed in [9].”
Convex Computation of the Region of Attraction of Polynomial Control Systems (2012, background): “The ROA can be computed analytically (see [27]) as , where”
Linear observer synthesis for nonlinear systems using Koopman Operator framework (2016, methodology): “Along similar lines, necessary and sufficient relationships between the existenc of specific eigenfunctions of the Koopman operator and th global stability property of fixe points and limit cycles have been established in (Mauroy and Mezic (2013, Unpublished)). Numerical methods to estim te the regi”
Stochastic Optimal Control and Linear Programming Approach (2011, methodology): “Linear programming tools have been efficiently used before to deal with stochastic control problems (see Basak et al. [2], Bhatt, Borkar [3], Finlay [8], Hernandez-Lerma, Lasserre [14], Kurtz, Stockbridge [15], Lasserre [ 16 ], Stockbridge [19], Yin, Zhang [20] and references therein).”