Reza Ghaemi

Implicit Model Predictive Control of a Full Bridge DC–DC Converter

This paper presents a model predictive control (MPC)-based approach for a full bridge dc-dc converter of a fuel cell power system. The objective of the proposed control algorithm is to regulate the output voltage without violating the peak current constraint. We first develop a large signal dynamic model for the full bridge dc-dc converter. The peak current protection requirement is then formulated as a mixed input and state constraint for the MPC scheme. We next introduce the integrated perturbation analysis and sequential quadratic programming (InPA-SQP) method to solve the constrained optimal control problem with sub-millisecond level sampling time. The InPA-SQP solver can meet the computational efficiency demand, thereby enabling implementation of an implicit MPC for power electronics system with fast dynamics. The effectiveness of the proposed control algorithm in the peak current protection and the output voltage regulation has been verified with experimental results.

Brief paper: An integrated perturbation analysis and Sequential Quadratic Programming approach for Model Predictive Control

Computationally efficient algorithms are critical in making Model Predictive Control (MPC) applicable to broader classes of systems with fast dynamics and limited computational resources. In this paper, we propose an integrated formulation of Perturbation Analysis and Sequential Quadratic Programming (InPA-SQP) to address the constrained optimal control problems. The proposed algorithm combines the complementary features of perturbation analysis and SQP in a single unified framework, thereby leading to improved computational efficiency and convergence property. A numerical example is reported to illustrate the proposed method and its computational effectiveness.

Model Predictive Control for a Full Bridge DC/DC Converter

This paper investigates the implementation of both linear model predictive control (LMPC) and nonlinear model predictive control (NMPC) to a full bridge dc/dc converter under starting, overload, and load step change conditions. The control objective is to regulate the output voltage without violating the peak current constraint. The integrated perturbation analysis and sequential quadratic programming method is employed to solve the nonlinearly constrained optimal control problems with 300 μ s sampling time. The experimental results reveal that both the LMPC and NMPC schemes can successfully achieve voltage regulation and peak current protection. The experimental results are reported and several observations, seemingly counterintuitive, are analyzed to offer insight into the use of MPC for these challenging applications.

A method for determining the robustness of bio-molecular oscillator models.

BackgroundQuantifying the robustness of biochemical models is important both for determining the validity of a natural system model and for designing reliable and robust synthetic biochemical networks. Several tools have been proposed in the literature. Unfortunately, multiparameter robustness analysis suffers from computational limitations.ResultsA novel method for quantifying the robustness of oscillatory behavior to parameter perturbations is presented in this paper. This method relies on the combination of Hopf bifurcation and Routh-Hurwitz stability criterion, which is widely applied in control system design. The proposed method is employed to calculate the robustness of two oscillating biochemical network models previously analyzed in the literature. The robustness bounds here obtained are tighter than what was previously obtained in the literature for both models.ConclusionThe method here proposed for quantifying the robustness of biochemical oscillator models is computationally less demanding than similar multiparamter variation techniques available in the literature. It also provides tighter bounds on two models previously analyzed in the literature.

Brief paper: A stable block model predictive control with variable implementation horizon

In this paper, we present a stable receding horizon model predictive control for discrete-time nonlinear systems. The standard MPC scheme is modified to incorporate (1) a block implementation scheme where a string of the optimized input is applied instead of a single value; (2) an additional constraint which guarantees that a Lyapunov function decreases over time; (3) a variable implementation window that facilitates the constraints enforcement. Stability of the closed-loop system with the proposed algorithm is established. Examples and simulation results are given to illustrate the effectiveness of the control scheme. The impacts of several key design parameters on the overall performance are also analyzed and discussed.

Neighboring Extremal Solution for Nonlinear Discrete-Time Optimal Control Problems With State Inequality Constraints

A neighboring extremal control method is proposed for discrete-time optimal control problems subject to a general class of inequality constraints. The approach is applicable to a broad class of systems with input and state constraints, including two special cases where the constraints depend only on states but not inputs and the constraints are over determined. A closed form solution for the neighboring extremal control is provided and a sufficient condition for existence of the neighboring extremal solution is specified.

Control for Safety Specifications of Systems With Imperfect Information on a Partial Order

In this paper, we consider the control problem for uncertain systems with imperfect information, in which an output of interest must be kept outside an undesired region (the bad set) in the output space. The state, input, output, and disturbance spaces are equipped with partial orders. The system dynamics are either input/output order preserving with output in R2 or given by the parallel composition of input/output order preserving dynamics each with scalar output. We provide necessary and sufficient conditions under which an initial set of possible system states is safe, that is, the corresponding outputs are steerable away from the bad set with open loop controls. A closed loop control strategy is explicitly constructed, which guarantees that the current set of possible system states, as obtained from an estimator, generates outputs that never enter the bad set. The complexity of algorithms that check safety of an initial set of states and implement the control map is quadratic with the dimension of the state space. The algorithms are illustrated on two application examples: a ship maneuver to avoid an obstacle and safe navigation of an helicopter among buildings.

Robust control of ship fin stabilizers subject to disturbances and constraints

This paper is concerned with constrained roll control of ship fin stabilizers operating in wave fields. Our approach is based on a robust control algorithm for linear discrete-time systems subject to bounded additive disturbances and a general class of input-state constraints. The proposed method is applied to control of fin stabilizers. Simulation results show that the proposed robust control method reduces the ship roll motion while satisfying the input and dynamic stall constraints. The proposed control algorithm does not involve on-line optimization, except for a linear program solved at initialization. On the theory side, we present a generalized form of our robust constrained control algorithm to the case of mixed state-input constraints.

Model Predictive Control for Constrained Discrete Time Systems: An Optimal Perturbation Analysis Approach

In the paper we consider a model predictive control (MPC) strategy based on approximating the MPC optimal control solution by a nominal solution (either pre-computed in advance on-line or computed off-line) and a perturbation solution, which is easily computable and corrects the nominal solution. Unlike similar approaches in prior literature (see e.g., (A.E. Bryson and Y. Ho, 1975), (F.L. Lewis, 1986)), our approach is capable of enforcing piecewise state and control constraints. We describe how the basic approach can be integrated within the framework of forecasting MPC (FMPC) and illustrate its effectiveness by means of an example.

Robust Control of Constrained Linear Systems With Bounded Disturbances

This technical note develops a novel robust control algorithm for linear systems subject to additive and bounded disturbances. The approach is based on the constraint tightening method. While this problem can be tackled using existing robust model predictive control techniques, the proposed method has an advantage in that it is computationally efficient and avoids the need to solve repeatedly an online optimization problem, while the optimization problem solved at initialization is a simple linear programming problem. The algorithm elaborated in this technical note guarantees convergence to a minimal disturbance invariant set, and the terminal predicted state constraint set is allowed to be larger than the minimal disturbance invariant set. As an illustration, the developed algorithm is applied to constrained roll control of a ship operating in a wave field. Simulation results show that the proposed approach reduces the ship roll motion while the input and dynamic stall constraints are satisfied.