Prashant Mhaskar

Predictive control of switched nonlinear systems with scheduled mode transitions

In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: For each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing stability. The proposed control method is demonstrated through application to a chemical process example.

Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control ☆

This work considers the problem of stabilization of nonlinear systems subject to state and control constraints. We propose a Lyapunov-based predictive control design that guarantees stabilization and state and input constraint satisfaction from an explicitly characterized set of initial conditions. An auxiliary Lyapunov-based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. For the case when the state constraints are soft, we propose a switched predictive control strategy that reduces the time for which state constraints are violated, driving the states into the state and input constraints feasibility region of the Lyapunov-based predictive controller. We demonstrate the application of the Lyapunov-based predictive controller designs through a chemical process example.

Isolation and handling of actuator faults in nonlinear systems

This work considers the problem of control actuator fault detection and isolation and fault-tolerant control for a multi-input multi-output nonlinear system subject to constraints on the manipulated inputs and proposes a fault detection and isolation filter and controller reconfiguration design. The implementation of the fault detection and isolation filters and reconfiguration strategy are demonstrated via a chemical process example.

Predictive control of transport-reaction processes

This work focuses on the development of computationally efficient predictive control algorithms for nonlinear parabolic and hyperbolic PDEs with state and control constraints arising in the context of transport-reaction processes. We first consider a diffusion-reaction process described by a nonlinear parabolic PDE and address the problem of stabilization of an unstable steady-state subject to input and state constraints. Galerkin’s method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDE, which are subsequently used for controller design. Various model predictive control (MPC) formulations are constructed on the basis of the finite dimensional approximations and are demonstrated, through simulation, to achieve the control objectives. We then consider a convection-reaction process example described by a set of hyperbolic PDEs and address the problem of stabilization of the desired steady-state subject to input and state constraints, in the presence of disturbances. An easily implementable predictive controller based on a finite dimensional approximation of the PDE obtained by the finite difference method is derived and demonstrated, via simulation, to achieve the control objective.

Robust hybrid predictive control of nonlinear systems

In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability region within which any available MPC formulation can be implemented. This is achieved by devising a set of switching laws that orchestrate switching between MPC and the bounded robust controller in a way that exploits the performance of MPC whenever possible, while using the bounded controller as a fall-back controller that can be switched in at any time to maintain robust closed-loop stability in the event that the predictive controller fails to yield a control move (due, e.g., to computational difficulties in the optimization or infeasibility) or leads to instability (due, e.g., to inappropriate penalties and/or horizon length in the objective function). The implementation and efficacy of the robust hybrid predictive control structure are demonstrated through simulations using a chemical process example.

Model-based control of particulate processes

In this work, we present an overview of recently developed methods for model-based control of particulate processes. We primarily discuss methods developed in the context of our previous research work and use examples of crystallization, aerosol and thermal spray processes to motivate the development of these methods and illustrate their application. Specifically, we initially discuss control methods for particulate processes which utilize suitable approximations of population balance models to design nonlinear, robust and predictive control systems and demonstrate their application to crystallization and aerosol processes. Finally, we discuss the issues of control problem formulation and controller design for high-velocity oxygen-fuel (HVOF) thermal spray processes and close with few thoughts on unresolved research challenges on control of particulate processes.

Predictive control of crystal size distribution in protein crystallization

This work focuses on the modelling, simulation and control of a batch protein crystallization process that is used to produce the crystals of tetragonal hen egg-white (HEW) lysozyme. First, a model is presented that describes the formation of protein crystals via nucleation and growth. Existing experimental data are used to develop empirical models of the nucleation and growth mechanisms of the tetragonal HEW lysozyme crystal. The developed growth and nucleation rate expressions are used within a population balance model to simulate the batch crystallization process. Then, model reduction techniques are used to derive a reduced-order moments model for the purpose of controller design. Online measurements of the solute concentration and reactor temperature are assumed to be available, and a Luenberger-type observer is used to estimate the moments of the crystal size distribution based on the available measurements. A predictive controller, which uses the available state estimates, is designed to achieve the objective of maximizing the volume-averaged crystal size while respecting constraints on the manipulated input variables (which reflect physical limitations of control actuators) and on the process state variables (which reflect performance considerations). Simulation results demonstrate that the proposed predictive controller is able to increase the volume-averaged crystal size by 30% and 8.5% compared to constant temperature control (CTC) and constant supersaturation control (CSC) strategies, respectively, while reducing the number of fine crystals produced. Furthermore, a comparison of the crystal size distributions (CSDs) indicates that the product achieved by the proposed predictive control strategy has larger total volume and lower polydispersity compared to the CTC and CSC strategies. Finally, the robustness of the proposed method (achieved due to the presence of feedback) with respect to plant-model mismatch is demonstrated. The proposed method is demonstrated to successfully achieve the task of maximizing the volume-averaged crystal size in the presence of plant-model mismatch, and is found to be robust in comparison to open-loop optimal control strategies.

Predictive control methods to improve energy efficiency and reduce demand in buildings

Abstract This paper presents an overview of results and future challenges related to temperature control and cost optimization in building energy systems. Control and economic optimization issues are discussed and illustrated through simulation examples. The paper concludes with results from model predictive control solutions and identification of important directions for future work.

Cell Population Modeling and Parameter Estimation for Continuous Cultures of Saccharomyces cerevisiae

Saccharomyces cerevisiae is known to exhibit sustained oscillations in chemostats operated under aerobic and glucose‐limited growth conditions. The oscillations are reflected both in intracellular and extracellular measurements. Our recent work has shown that unstructured cell population balance models are capable of generating sustained oscillations over an experimentally meaningful range of dilution rates. A disadvantage of such unstructured models is that they lack variables that can be compared directly to easily measured extracellular variables. Thus far, most of our work in model development has been aimed at achieving qualitative agreement with experimental data. In this paper, a segregated model with a simple structured description of the extracellular environment is developed and evaluated. The model accounts for the three most important metabolic pathways involved in cell growth with glucose substrate. As compared to completely unstructured models, the major advantage of the proposed model is that predictions of extracellular variables can be compared directly to experimental data. Consequently, the model structure is well suited for the application of estimation techniques aimed at determining unknown model parameters from available extracellular measurements. A steady‐state parameter selection method developed in our group is extended to oscillatory dynamics to determine the parameters that can be estimated most reliably. The chosen parameters are estimated by solving a nonlinear programming problem formulated to minimize the difference between predictions and measurements of the extracellular variables. The efficiency of the parameter estimation scheme is demonstrated using simulated and experimental data.

Lyapunov-based model predictive control of stochastic nonlinear systems

In this work, we design a Lyapunov-based model predictive controller (LMPC) for nonlinear systems subject to stochastic uncertainty. The LMPC design provides an explicitly characterized region from where stability can be probabilistically obtained. The key idea is to use stochastic Lyapunov-based feedback controllers, with well characterized stabilization in probability, to design constraints in the LMPC that allow the inheritance of the stability properties by the LMPC. The application of the proposed LMPC method is illustrated using a nonlinear chemical process system example.