Constrained control for systems on matrix Lie groups with uncertainties

For the input and output constraints and uncertainties in batch processes, a 2D output feedback robust constrained model predictive control (MPC) method is designed by combining iterative learning control (ILC), MPC and output feedback. Firstly, an equivalent 2D-FM closed-loop prediction model is established by combining with the proposed output feedback controller. Then an optimization performance index function with terminal constraint is constructed to study its control optimization. According to the designed optimization performance index and Lyapunov stability theory, the feasible MPC problem is obtained by solving the linear matrix inequalities (LMIs). At the same time, the gain of the new output feedback control law is given to ensure that the performance index reaches the minimum upper bound under the constraints of input and output. In order to solve the manual adjustment problem of some parameters in the performance index function, the particle swarm optimization (PSO) algorithm is introduced, and a better solution is found near the controller by using the search optimization method. Finally, taking the injection molding process as an example and comparing with the existing method without using PSO algorithms, it is proved that the above method is more feasible.

This paper proposes an improved constrained networked model predictive tracking control design for the chamber pressure of a coke furnace under uncertainty and packet losses. Unlike conventional constrained model predictive control (MPC) strategies that have a limitation in the consideration of both set-point tracking and the dynamic process responses, the system state variables and output tracking errors are combined and thus can be regulated simultaneously in the new MPC scheme. Based on such advantages, there are more degrees of freedom for the subsequent controller design and improved system performance can then be obtained. Case studies on the regulation of chamber pressure of a coke furnace under process uncertainties and packet losses are investigated to verify the proposed approach in comparison with typical traditional constrained MPC schemes.

The availability of predictions of future system inputs has motivated research into preview control to improve set-point tracking and disturbance rejection beyond that achievable via conventional feedback control. The design of preview controllers, typically based upon model predictive control (MPC) for its constraint handling properties, is often performed in a monolithic nature, coupling the feedback and feed-forward problems. This can create problems, such as: (i) an additional feedback loop is introduced by MPC, which alters the closed-loop dynamics of the existing feedback compensator, potentially resulting in a deterioration of the nominal sensitivities and robustness properties of an existing closed-loop and (ii) the default preview action from MPC can be poor, degrading the original feedback control performance. In our previous work, the former problem is addressed by presenting a modular MPC design on top of a given output-feedback controller, which retains the nominal closed-loop robustness and frequency-domain properties of the latter, despite the addition of the preview design. In this paper, we address the second problem; the preview compensator design in the modular MPC formulation. Specifically, we derive the key conditions that ensure, under a given closed-loop tuning, the preview compensator within the modular MPC formulation is systematic and well-designed in a sense that the preview control actions complement the existing feedback control law rather than opposing it. In addition, we also derive some important results, showing that the modular MPC can be implemented in a cascade over any given linear controllers and the proposed conditions hold, regardless of the observer design for the modular MPC. The key benefit of the modular MPC is that the preview control with constraint handling can be implemented without replacing the existing feedback controller. This is illustrated through some numerical examples.

In this paper, robust constrained model predictive control of uncertain fuzzy affine systems is considered. Based on piecewise quadratic Lyapunov functions, highly efficient robust constrained predictive control approaches are developed so that the closed-loop stability is guaranteed, and the transient control performance is improved even under input or state constraints. Moreover, by using approximate ellipsoid and S -procedure, the solution to the fuzzy affine model based predictive control can be cast as a convex optimization problem subject to some linear matrix inequalities, rather than a nonconvex problem via bilinear matrix inequalities as in conventional fuzzy affine model-based control. The proposed controllers are thus easier for real-time implementation in industry. Simulation results on the fluidized bed combustion plant have demonstrated the performance of the proposed approaches.

Extending fuel cell lifetime is a necessary objective for reducing fuel cell power generation cost of electricity. Capital costs comprise the most significant fraction of the cost of electricity. Reducing the frequency of fuel cell replacement can be achieved by implementing a control strategy that prevents excursions into operating regions causing failure. In this paper we implement a constrained MIMO model predictive controller (MPC) to avoid the failure modes relevant for a high-temperature tubular solid oxide fuel cell (SOFC) system while performing load-following. The primary causes of failure are catalyst poisoning, fuel or air starvation, carbon deposition, and microcracking. Prior steady-state thermomechanical stress analysis in literature has demonstrated that the minimum cell temperature and maximum negative radial thermal gradient are primary causes of microcracking in the SOFC. State-of-the-art SOFC control literature often seeks to track a mean or outlet cell temperature. The authors have presented the first approach to control the primary two causes of thermally-driven microcracking in tubular SOFCs using constrained control. Constraints are also incorporated into a steady-state optimization to ensure a feasible optimum.

In this paper, we address the problem of synthesizing output feedback control law for constrained linear systems. For lack of state information, the plant states will be estimated by an observer. Using the Lyapunov function of estimated plant and controller states, the constrained output feedback control problem will be formulated and solved in terms of linear matrix inequalities (LMIs). The quadratic cost function is minimized over control policies to yield an output feedback control strategy subject to input/output constraints. Both infinite-horizon and finitehorizon receding horizon control (RHC) are considered in the paper. Closed-loop stability and feasibility of RHC are guaranteed by off-line constrained control designs. The simulation results show that finite-horizon RHC provides better performance upper bound than infinite-horizon RHC.

M0638. In the paper, a dual-mode control strategy based on a self-triggered model predictive control (SMPC) and a state-feedback law is present for a continue linear time-invariant (LTI) system with state and input constrains. Compared with nominal model predictive control (NMPC), robustness is guaranteed to reject unknown disturbances for the system. At each triggering instant, the self-triggered mechanism is designed to compute the inter-execution time and reduce the frequency of solving the optimization problem and the communication. Then, the stability of the dual-mode strategy is analyzed to ensure the states practically stable. The theoretical results are verified by numerical simulation and the effects of parameters are discussed in detail.

The constraints of output variables, input variables and intermediate variables exist widely in chemical process control. The inconsistency in different constraints may make constrained model predictive controller have no feasible solutions, which will bring harmful effect to practical production. To ensure the implementation of model predictive control, using its global optimization performance and constraint handling mechanism, a new particle-swarm optimization algorithm with the function of constraint handling, was proposed in this article. Taking into account the form of constraints and the constraints characteristics of MIMO (multi-input multi-output) predictive control system, this thesis, based on convex polyhedron geometry, discuss the feasibility of constrained model predictive control. Combined with duality theorem, the output constraints of system are transformed into constraints of input. After that, the constraints form which meets the requirements of control algorithm is obtained. Finally, particle swarm optimization algorithm is used to conduct the optimization of predictive control system. The simulation results of MIMO model with constraints showed the advantages and effectiveness of this algorithm.

This paper introduces a quasi‐linear parameter‐varying model predictive control (qLPV MPC) framework for robust trajectory tracking of fully actuated unmanned underwater vehicles (UUVs), explicitly considering external disturbances and input constraints. To address the challenges of nonlinear dynamics, actuator limitations, and external disturbances, the UUV system is formulated as a qLPV model to balance the computational efficiency and the control accuracy. Then, a qLPV MPC method is designed for UUVs by incorporating an auxiliary feedback control law and a terminal constraint set, which ensures iterative feasibility and asymptotic stability. The input‐to‐state stability (ISS) is mathematically proven through Lyapunov‐based analysis, so that the proposed framework could stabilize bounded tracking errors despite system disturbances. Finally, an iterative solution method based on sequential quadratic programming (SQP) is introduced to obtain efficient solutions of the optimal control sequence while reducing the computational complexity. Simulation studies are conducted to validate the effectiveness of the proposed controller. The results show that the proposed method exhibits smaller tracking errors and faster convergence speeds compared to traditional robust nonlinear model predictive control (NMPC).

Model predictive control (MPC) is a popular optimal control approach that can explicitly deal with system constraints. However, its high computational cost motivates researches on various approximation methods that make the MPC more practically viable for systems with fast dynamics and/or limited on-board computing power. Neighboring extremal (NE) is one such method that can be used to adapt to a nominal open-loop MPC sequence based on state perturbations so that it alleviates the online computational burden and extends the applicability of the MPC. In this paper, a cloud-based nonlinear MPC (NMPC) framework is considered where the NMPC is first performed on the cloud by taking advantage of its powerful computation and storage capabilities. To save the computational power, instead of solving the NMPC problem at every time step, the open-loop control sequence is downloaded for on-board implementation, then the NE is employed to systematically update the control sequence based on the deviation of the measured/estimated state from the nominal state obtained by the cloud-based NMPC. However, due to unknown disturbances and request-response communication delays between the plant and the cloud, the cloud-based NMPC may not show a reasonable performance for the plant even with the NE adaptations when the deviation is large. Therefore, we develop an event-triggered scheme based on a cost criteria to strike a balance between performance and cost. Finally, the efficacy of the proposed control synthesis is demonstrated with simulations on the application of the cart inverted pendulum.

The automation of a truck-trailer offers enormous potential for safe and efficient transportation. The optimal control approaches, e.g., MPC, have significantly improved the tracking accuracy and the smoothness of the lateral control of vehicles. MPC application for a truck-trailer is complex compared to a car as the system behavior is different for forwarding and reversing. In this paper, we propose a lateral MPC algorithm for a truck-trailer, where we linearize the system dynamics around a nominal trajectory computed using a control law. The control law formulated as cascade control computes the nominal trajectory, an initial guess to the optimization process. The nominal trajectory lies in the vicinity of the optimal trajectory. We linearize the system dynamics around the computed nominal trajectory, reducing the linearization errors. The region of validity of the linearized system dynamics is narrow due to the system’s instability during reverse driving. A quadratic optimization problem subjective to the linear dynamics of the truck-trailer and state and input constraints defines the optimal control problem. The nominal trajectory is stable over the prediction horizon while reversing, so is the linear prediction model, improving optimization feasibility. Further, the discretization errors are also reduced using a small discrete step and integrating the model multiple times between two prediction steps. We tested the developed MPC approach on a prototypical full-scale truck-trailer system and discussed results. The developed MPC is considerably fast and accurate for real-time application.

PurposeThe purpose of this paper is to show the feasibility of constrained model predictive control (MPC) for sophisticated helicopter models which are derived by physical considerations.Design/methodology/approachPhysics‐based modeling is used to create control‐oriented helicopter models. Advanced constrained controllers are designed and tested for these sophisticated models.FindingsThe helicopter models are valid and constrained MPC shows considerable promise for robust tracking.Practical implicationsMPCs can be implemented for highly constrained helicopter flights.Originality/valueA complete process of control‐oriented, physics‐based model development for helicopters followed by MPC design is developed. It is also proved that constrained MPC can be used and implemented online to robustly track discontinuous helicopter trajectories with heterogeneous constraints, even when the models are sophisticated and physics based.

In this paper, a model predictive control (MPC) strategy for nonlinear homogeneous reaction systems is proposed. The nonlinear system is first transformed to a linear parameter varying (LPV) system by means of a linear transformation known as extents decomposition. The resulting LPV system is further converted to a linear time invariant (LTI) system by means of a parametric state feedback and feedforward control laws. The use of this description results in linear MPC with a quadratic performance index and nonlinear state parameter constraints. However, based on the polytopic nature of the parameter of the LPV systems, the constraints are transformed to a set of intersected polyhedrons. The final result is a linear MPC problem with linear constraints that can be easily converted and solved as a quadratic programming problem. Finally, the performance of the control strategy is illustrated in simulation and compared with a controller based on a constant-parameter LTI model.

A model predictive controller (MPC) is proposed, which is robustly stable for some classes of model uncertainty and to unknown disturbances. It is considered as the case of open-loop stable systems, where only the inputs and controlled outputs are measured. It is assumed that the controller will work in a scenario where target tracking is also required. Here, it is extended to the nominal infinite horizon MPC with output feedback. The method considers an extended cost function that can be made globally convergent for any finite input horizon considered for the uncertain system. The method is based on the explicit inclusion of cost contracting constraints in the control problem. The controller considers the output feedback case through a non-minimal state-space model that is built using past output measurements and past input increments. The application of the robust output feedback MPC is illustrated through the simulation of a low-order multivariable system.

Stability is perhaps the most important property of controllers. A stable controller performs its task reliably in any circumstance; however, an unstable controller may cause system failure with dramatic effects. Unstable controllers in an active vibration control (AVC) system may even cause structural failure. Stability can be guaranteed and studied in traditional control systems by inspecting the location of the closed-loop poles of the transfer function, or equivalently the magnitude of the eigenvalues of the state matrix. Unfortunately, the constrained model predictive control (MPC) law is nonlinear and it cannot be expressed in a closed form. Considering the cost function as a Lyapunov function is the key to understand the stability of the constrained MPC strategy. As long as the cost function is monotonically decreasing, the control process remains stable. It can be proved that the condition for this is to ensure the feasibility of the input sequence from the current time up to infinity. Fortunately, this seemingly formidable task can be implemented with a finite number of optimization variables. An additional constraint checking horizon in infinite horizon cost dual-mode constrained MPC ensures stability and feasibility. The series of additional constraints to ensure stability also allocate a special region of state-space called the region of attraction and its subset, the target set. For an optimal MPC strategy with maximum performance, these have a complex polyhedral shape. In the interest decreasing complexity and increasing computational speeds, these sets can be simplified to low complexity hypercubes or a hyperellipsoids. This chapter reviews the stability properties of the constrained MPC control law, how it can be guaranteed at all times, introduces the reader to maximal invariant target sets and some of its simplified approximations.