Abstract. 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)-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.
From this infinite-dimensional LP, REF defines hierarchies of Linear Matrix Inequalities (LMI) relaxations, to synthesise a sequence of polynomial controls converging to the solutions of the optimal control problem.
Nonlinear optimal control via occupation measures and LMI relaxations
SIAM Journal on Control and Optimization
Mathematics Computer Science