Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations

We consider the class of nonlinear optimal control problems (OCP) 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)-relaxa...

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M ar 2 00 7 NONLINEAR OPTIMAL CONTROL VIA OCCUPATION MEASURES AND LMI - RELAXATIONS

We consider the class of nonlinear optimal control problems (OCP) 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)-relaxa...

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Modal occupation measures and LMI relaxations for nonlinear switched systems

This paper presents a linear programming approach for the optimal control of nonlinear switched systems where the control is the switching sequence. This is done by introducing modal occupation measures, which allow to relax the problem as a primal linear programming (LP) problem. Its dual linear program of HamiltonJacobi-Bellman inequalities is also characterized. The LPs are then solved numer...

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Nonlinear optimal control: Numerical approximations via moments and LMI-relaxations

We consider the class of nonlinear optimal control problems with all data (differential equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of LMI-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Preliminary results show that good approximations are obtained with few moments.

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Modal occupation measures and LMI relaxations for nonlinear switched systems control

This paper presents a linear programming approach for the optimal control of nonlinear switched systems where the control is the switching sequence. This is done by introducing modal occupation measures, which allow to relax the problem as a primal linear programming (LP) problem. Its dual linear program of HamiltonJacobi-Bellman inequalities is also characterized. The LPs are then solved numer...

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Nonlinear Optimal Control via Occupation Measures and LMI-Relaxations

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