Dual MPC Research Articles

Development of a Distributed Adaptive Dual MPC Scheme with Application to Control of an Octuple Tank System

The distributed model predictive control (dMPC) provides a computationally efficient framework for designing controllers for a large dimensional plant. The performance of such dMPC scheme critically depends upon the quality of the control relevant models used for predictions. In continuously operated processes, model plant mismatch (MPM) arises due to the time-varying nature of process parameters and shift in the operating conditions due to economic considerations and this results in performance degradation. Recently an adaptive version of dMPC (dAMPC) has been developed that achieves better control performance using online model parameter update. A conventional adaptive MPC scheme, however, requires external dither signal to be injected to generate sufficient excitation needed for parameter estimation. In this work, dAMPC is cast in the dual control framework (dADMPC) which ensured sufficient input excitation as and when needed for better online parameter estimation. The proposed controller is based on black-box models parameterized using generalized orthogonal basis filters (GOBF). The Fourier coefficients of the GOBF models are dynamically updated online using recursive parameter estimators to account for MPM. The efficacy of the proposed scheme is demonstrated by simulating servo and regulatory problems associated with the benchmark octuple tank process. The simulation study reveals that performance of the proposed dADMPC scheme is comparable to a centralized ADMPC while achieving a considerable reduction in the online computation time.

Development of an adaptive and explicit dual model predictive controller based on generalized orthogonal basis filters

A significant fraction of industrial MPC schemes employs linear prediction models. Closed loop performance of a linear model based MPC scheme can deteriorate over a period of time if the prediction model is not updated to account for the changing operating conditions. An effective way of handling this problem is to employ dual control, which directs the plant output towards a reference setpoint and simultaneously injects probing signals into the plant to get information-rich data which can be used for model identification under closed loop conditions. In this work, two multivariable adaptive dual MPC (ADMPC) schemes are developed based on MISO output error models that are parameterized using generalized orthonormal basis filters (GOBF). A nominal model is initially developed using offline identification exercise. The Fourier coefficients of the GOBF models are subsequently updated online using recursive parameter estimators. Also, to deal with large magnitude changes in the operating conditions, a shifting time window based approach is developed that can track variations of the GOBF poles online. To begin with, starting from a stochastic infinite horizon constrained optimal control problem, a computationally tractable finite horizon surrogate of the optimal control problem is derived. The surrogate problem includes terms that are sensitive to the parameter covariance. Based on the surrogate optimal control problem, two variants of ADMPC are proposed, viz. one that uses a fixed Fourier basis and another that uses a time varying Fourier basis. The effectiveness of the ADMPC schemes is evaluated by conducting stochastic simulations and experimental studies on the benchmark quadruple tank process. Analysis of the simulation results reveals that the proposed ADMPC schemes are able to achieve better tracking and regulatory performances when compared to the conventional adaptive MPC (AMPC). The simulation exercise also reveals that the proposed approach provides sufficient degrees of freedom to excite the plant in the closed loop for generating information-rich data for online model update. Experimental validation demonstrates that the proposed ADMPC is able to inject higher levels of input excitation throughout servo and regulatory responses with excitation levels similar to excitation levels used in the open loop identification experiments.

An Adaptive Dual MPC Scheme based on Output Error Models Parameterized using Generalized Orthonormal Basis Filters

A significant fraction of industrial MPC schemes employ linear prediction models. Closed loop performance of a linear model based MPC scheme can deteriorate over a period of time if the prediction model is not updated to account for the changing operating conditions. A possible remedy to this problem is on-line update of the model parameters under the closed loop conditions. An effective way of handling this problem is through dual control, which directs the plant output towards a reference setpoint and simultaneously injects probing signals into the plant to get information-rich data. In this work, an adaptive dual MPC scheme is developed for controlling MIMO systems based on output error models (OE) parameterized using generalized orthogonal basis filters (GOBF). A nominal model is initially developed using o-ine identification exercise. The Fourier coe¢cients of GOBF-OE models are then updated online using recursive least squares algorithm. Similar to Kumar et al. [2015], the MPC formulation is modified to include terms that are sensitive to the parameter covariance and are capable of injecting probing perturbations into the system as and when required. A distinguishing feature of the proposed work is the use of state space realizations of GOBF networks for model development and prediction. Simulation studies using the benchmark quadruple tank system (Johansson [2000]) reveal that the proposed approach provides su¢cient degrees of freedom to excite the plant in closed loop for generating information rich data for model parameter estimation.

Dual MPC with Reinforcement Learning

An adaptive optimal control algorithm for systems with uncertain dynamics is formulated under a Reinforcement Learning framework. An embedded exploratory component is included explicitly in the objective function of an output feedback receding horizon Model Predictive Control problem. The optimization is formulated as a Quadratically Constrained Quadratic Program and it is solved to e-global optimality. The iterative interaction between the action specified by the optimal solution and the approximation of cost functions balances the exploitation of current knowledge and the need for exploration. The proposed method is shown to converge to the optimal policy for a controllable discrete time linear plant with unknown output parameters.

Experimental Evaluation of a MIMO Adaptive Dual MPC

Maintaining uniformly satisfactory control performance of an MPC scheme in the face of changing operating conditions is a difficult task. An adaptive MPC scheme that directs the output towards a reference and simultaneously injects a probing signal to get more information about the system for better model identification appears to be ideally suited for achieving this goal. In this work, taking motivation from the dual control problem originally developed by Feldbaum [1960], a MIMO adaptive dual MPC (adaptive DMPC) formulation has been proposed, which does not require external probing signals to improve the model parameter estimates. The objective function of the MPC is modified to include terms that ensure that sufficient excitation is injected into the system while performing the control tasks. The efficacy of the proposed adaptive DMPC formulation is evaluated by conducting experimental studies on the benchmark heater mixer system. The experimental results demonstrate that the proposed formulation is able to inject probing inputs of small magnitude while meeting the desired servo and regulatory control objectives.