Discrete-Time Optimal Control Ensuring Fixed-Time Prescribed Performance for SSP

Current prescribed performance optimal controllers focus on continuous-time systems, leaving a gap in discrete-time optimal control with prescribed performance guarantees. This work explores a discrete-time optimal control protocol ensuring fixed-time prescribed quality, applied to the seeker stabilized platform (SSP). To achieve this, we define an asymptotically convergent iterative update for transformed errors using fixed-time performance functions, leading to the construction of a variable for a discrete-time dynamic system distinct from the original. This variable is then used to define a cost function, minimized using the value-iteration-driven dynamic programming approach. Convergence proof demonstrates that both the cost function and control protocol ultimately converge to their optimal values, guaranteeing the fixed-time prescribed transient and steady-state behaviors in discrete time. Finally, a comparative simulation on SSP validates the design.