Nonlinear Optimal and Constrained Trajectory Tracking based on Control Lyapunov Function

The purpose of this paper is the optimal and constrained nonlinear optimization-based tracking strategy using Control Lyapunov Function (CLF) technique. The main approach is based on analytical solution and guarantees that the closed-loop system is stable, whilst presenting an explicit relation for the controller. A CLF method-base that considers the cost function in the design process is referred to as "Satisficing" method. In this method, optimal control problem is not solved directly. Instead, it's tried to design the control law point-wise so that a utility function is greater than a penalty function. Thus, its implication results in optimality of the performance objective in control strategies. The main disadvantage of Satisficing method is the lack of stability guarantee in systems with bounded control input. Referring to significance of bounded input in real systems, it's attempted to amend the method in order to overcome the said drawback. Therefore, after reviewing the Satisficing method, the modified method is proposed and attempted to prove its optimality and boundedness. Simulation results show that using the proposed method, a reference trajectory is well followed and while the input remains within its bounds.