Extremum-seeking control of state-constrained nonlinear systems

An extremum-seeking control problem is posed for a class of nonlinear systems with unknown dynamical parameters, whose states are subject to convex, pointwise inequality constraints. Using a barrier function approach, an adaptive method is proposed for generating setpoints online which converge to the feasible minimizer of a convex objective function containing the unknown dynamic parameters. A tracking controller regulates system states to the generated setpoint via state feedback, while maintaining feasibility of the state constraints. A simulation example demonstrates application of the method.