(748d) Output Feedback Regulation Via Carleman Based Receding Horizon Estimation and Control

We present an algorithm that combines Carleman moving horizon estimation (CMHE) with Carleman model predictive control (CMPC) to design an output feedback receding horizon controller. CMHE identifies the system state and noise terms from noisy measurements, based on measurement history and process model. The identified process state is then provided as the initial condition to CMPC, which then makes optimal control decisions based on predications made via the process model. The first decision is then enacted on the process and the optimal control decisions made by the CMPC update the dynamic model used in the CMHE to increase the precision of the estimations. The novelty in our contribution lies in modeling the nonlinear dynamics with Carleman approximation, which allows us to estimate the system evolution for both CMHE and CMPC analytically. The Gradient vectors and Hessian matrices are then provided to facilitate the optimizations by these observer controller designs. To further reduce real-time computation, we adapt the advanced-step NMHE and advanced-step NMPC concepts ¹² to our CMHE/CMPC pair to develop an asCMHE/asCMPC pair. The new design pre-estimates the states and pre-designs the manipulated input sequence one step in advance of real-time using the analytical solutions to the process model, and then it updates the estimation and control decisions almost in the real-time using pre-calculated analytical sensitivities of the estimation and control solutions to the system state.

A nonlinear open-loop unstable CSTR is studied as the illustration example. Any small perturbation in the operating condition may cause large oscillations on both the concentration and the reactor temperature. Under unmeasured process and sensor noises, both the concentration and the temperature go through a periodic orbit away from the desired steady state. With output feedback control, the closed-loop system identifies the noise and the state, regulates the system back to the desired temperature. Using standard nonlinear MHE/nonlinear MPC, the controller takes more than one sampling time to make a decision, which is infeasible in practice. With the CMHE/CMPC pair, computational time is decreased twentyfold to 7.48 % of one sampling time. With asCMHE/asCMPC pair, the computational time of estimation and control is further reduced to a negligible amount in terms of on-time calculation ³.

Reference:

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3. Fang Y, Armaou A. Output Feedback Receding Horizon Regulation via Moving Horizon Estimation and Model Predictive Control. Submitted to J Process Control. 2018