Constrained stabilization of a continuous stirred tank reactor via smooth control Lyapunov R-functions

The constrained stabilization of the multivariable nonlinear model of a continuous stirred tank reactor is addressed. In this control setting, the novel class of control Lyapunov R-functions is proposed to design a smooth control Lyapunov function having external level set in accordance to the state constraints and non-homothetical inner level sets arbitrarily close to the desired (optimal) ones. The flexibility in shaping the composite control Lyapunov function is obtained by introducing a novel composition rule. The simulation of an exothermic chemical process shows the benefits of using a control Lyapunov R-function together with a gradient-based nonlinear controller, in fact a much larger controlled invariant state space set is obtained, moreover better state convergence and smoother control inputs are recovered.