Off-line approach to dynamic output feedback robust model predictive control

For quasi-linear parameter varying (quasi-LPV) systems with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with the consideration of input saturation is investigated. The saturated dynamic output feedback controller is represented by a convex hull involving the actual dynamic output controller and an introduced auxiliary controller. By taking both the actual output feedback controller and the auxiliary controller with a parameter-dependent form, the main optimization problem can be formulated as convex optimization. The consideration of input saturation in the main optimization problem reduces the conservatism of dynamic output feedback controller design. The estimation error set and bounded disturbance are represented by zonotopes and refreshed by zonotopic set-membership estimation. Compared with the previous results, the proposed algorithm can not only guarantee the recursive feasibility of the optimization problem, but also improve the control performance at the cost of higher computational burden. A nonlinear continuous stirred tank reactor (CSTR) example is given to illustrate the effectiveness of the approach.

ABSTRACTThe output feedback robust model predictive control (MPC), for the linear parameter varying (LPV) system with norm-bounded disturbance, is addressed, where the model parametric matrices are only known to be bounded within a polytope. The previous techniques of norm-bounding technique, quadratic boundedness (QB), dynamic output feedback, and ellipsoid (true-state bound; TSB) refreshment formula for guaranteeing recursive feasibility, are fused into the newly proposed approaches. In the notion of QB, the full Lyapunov matrix is applied for the first time in this context. The single-step dynamic output feedback robust MPC, where the infinite-horizon control moves are parameterised as a dynamic output feedback law, is the main topic of this paper, while the multi-step method is also suggested. In order to strictly guarantee the physical constraints, the outer bound of the true state replaces the true state itself, so tightness of this bound has a major effect on the control performance. In order to tighten the TSB, a procedure for refreshing the real-time ellipsoid based on that of the last sampling instant is given. This paper is conclusive for the past results and far-reaching for the future researches. Two benchmark examples are given to show the effectiveness of the novel results.

This article provides a solution to tube-based output feedback robust model predictive control (RMPC) for discrete-time linear parameter varying (LPV) systems with bounded disturbances and noises. The proposed approach synthesizes an offline optimization problem to design a look-up table and an online tube-based output feedback RMPC with tightened constraints and scaled terminal constraint sets. In the offline optimization problem, a sequence of nested robust positively invariant (RPI) sets and robust control invariant (RCI) sets, respectively, for estimation errors and control errors is optimized and stored in the look-up table. In the online optimization problem, real-time control parameters are searched based on the bounds of time-varying estimation error sets. Considering the characteristics of the uncertain scheduling parameter in LPV systems, the online tube-based output feedback RMPC scheme adopts one-step nominal system prediction with scaled terminal constraint sets. The formulated simple and efficient online optimization problem with fewer decision variables and constraints has a lower online computational burden. Recursive feasibility of the optimization problem and robust stability of the controlled LPV system are guaranteed by ensuring that the nominal system converges to the terminal constraint set, and uncertain state trajectories are constrained within robust tubes with the center of the nominal system. A numerical example is given to verify the approach.

An improved off-line approach for output feedback robust model predictive control

SummaryThe present paper addresses an observer‐based output feedback robust model predictive control for the linear parameter varying system with bounded disturbance and noise subject to input and state constraints. The main contribution is that the on‐line convex optimization problem not only simultaneously optimizes the observer and controller gains to stabilize the augmented closed‐loop system but also incorporates the refreshment of bounds of the estimation error set. The optimization problem steers the nominal augmented closed‐loop system to converge to the origin, and the real augmented closed‐loop system bounded within robust positive invariant set converges to a neighborhood of the origin such that recursive feasibility of the optimization and robust stability of the controlled system are ensured. Two numerical examples are given to illustrate the effectiveness of the method.

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.

Effective recursive parallelotopic bounding for robust output-feedback control

An off-line output feedback MPC strategy for nonlinear systems represented by quasi-LPV model

A robust dynamic output feedback controller synthesis algorithm considering H∞/H2performance and regional pole placement is addressed for a nonlinear system with parameter uncertainties and external disturbance. First, the formulation of a gain‐scheduled mixed‐objective robust dynamic output feedback controller for continuous‐time polytopic linear parameter varying (LPV) systems is presented. To reduce conservativeness, some auxiliary slack variables and parameter‐dependent Lyapunov functions are employed in addition to well‐established performance conditions. Then, sufficient conditions for the desired gain‐scheduled mixed‐objective robust dynamic output feedback controllers are cast into an efficiently tractable finite‐dimensional convex optimization problem in terms of linear matrix inequalities (LMIs). Finally, numerical simulation shows the validity of the proposed controller, which has good stability, strong robustness, satisfied disturbance attenuation ability, and smooth dynamic properties.

A robust output feedback control which globally stabilizes a class of SISO minimum-phase nonlinear systems with known and constant relative degree containing a vector of unknown parameters is developed. The constant parameter vector is not restricted to enter linearly in the state equations but it is assumed to belong to a known compact set and an imprecise knowledge of the nonlinearities (e.g., lookup tables) is allowed. The class of nonlinear systems is determined by geometric conditions; an additional assumption, which generalizes the knowledge of the sign of high-frequency gain for linear systems, is also required. The nonlinearities are restricted to depend, in suitable coordinates, on the output only: no growth conditions, such as sector or Lipschitz, are required. The robust output feedback control stabilizes the system for every value of the parameter vector in a known compact set. The order of the compensator is equal to the relative degree minus one. >

A robust adaptive NN-based output feedback control scheme is presented for a dynamic positioning ship with uncertainties and unknown external disturbances. We tackle the problem that velocity vector of a ship is not available by employing a high-gain observer, and develop the proposed control approach by combing vectorial backstepping with dynamic surface control approach, which is simpler and easier to implement in engineering practice. The neural network (NN) approximation technique is used to compensate for the uncertainties and unknown external disturbances, and it removes the requirement for the prior knowledge about the vessel parameters and external disturbances. Also, it is demonstrated that the proposed control strategy can force the position and yaw angle of a dynamic positioning ship to approach the desired point while guaranteeing all singles of the designed closed-loop dynamic positioning system semi-globally uniformly ultimately bounded by means of the Lyapunov function. Simulation results of a supply ship illustrate the effectiveness of the proposed scheme.

The aim of this study was to design a constrained robust output feedback control strategy for stabilizing linear systems affected by uncertainties and output perturbations. The input is constrained by a saturation function. A classical Luenberger observer reconstructed the states from output observations. The state feedback control employed the estimated states given by the observer. This work proposed a Barrier Lyapunov Function (BLF) to manage the saturation problem in the control input. Moreover, an extended version of the attractive ellipsoid method (AEM) characterized the zone of convergence due the presence of perturbations in the output. A convex optimization procedure, formulated as a set of matrix inequalities, yielded the control parameters and the region of attraction for the close‐loop system as well as a minimal ultimately bounded set for the system trajectories. Numerical simulations supported the theoretical results formulated in this study.

The deployment of Autonomous Underwater Vehicles (AUVs) for ocean observation is one of the important methods in marine scientific research. The stability of AUV attitude control determines the efficiency and safety of underwater operations. In practical systems, the actuators carried by AUVs have saturation, and the saturation of the actuators greatly affects the performance and stability of AUV attitude control. This article designs an anti-windup [Formula: see text] robust state feedback controller and an anti-windup [Formula: see text] robust dynamic output feedback controller for the pitch attitude control of AUVs to solve the pitch attitude control problem of AUVs subject to input constraints. Firstly, building a Linear-parameter varying (LPV) model for the AUV. Then, we design two anti-windup [Formula: see text] robust controllers based on LPV model. Simulation results verify the reasonable of LPV model and the effectiveness of proposed controllers. Proposed controllers can enable the system to quickly reach the desired attitude under input constraints.

Dispatchable-virtual oscillator control (D-VOC) is a promising time-domain grid-forming (GFM) technology designed to emulate the dynamic behavior of physical oscillators. Large-signal stability (LSS) is a crucial aspect of power system planning, mainly concerning the ability of power sources to synchronize with each other following a disturbance. However, GFM transient stability analysis typically omits the influence of inner current control (ICC) and voltage control (VC), potentially resulting in inaccurate assessments. Indeed, this paper analyzes the impact of ICC, VC, and current reference angle on the LSS of D-VOC, determining that incorporating ICC, though improving the precision of stability evaluations, simultaneously constrains the region of attraction (RoA). Moreover, the RoA is characterized using both the general quadratic and polynomial Lyapunov functions. In order to address these challenges, this study proposes a sophisticated framework, namely adaptive D-VOC (AD-VOC), an enhancement of standard D-VOC that introduces an additional degree of freedom through outer loop feedback and ICC feedforward to support fault ride-through. The proposed control is compared with the D-VOC and virtual synchronous generator (VSG) GFMs and numerical simulations show that the AD-VOC performs better than the traditional D-VOC and VSG in terms of adaptability, stability, and flexibility during short-circuit and load variation disturbances, marked by a substantial improvement in the RoA and accelerated dynamic response. Consequently, the proposed method not only reduces the overall cost associated with power electronics converters but also extends their operational lifespan. The proposed approach is further validated by implementing the AD-VOC in a lab-scale microgrid running in real-time.

A problem of designing an output feedback controller to improve transient performance in uncertain linear time-varying systems subjected to bounded external disturbances is considered. For systems with the dynamics specified by polytopic uncertainties, we design linear reduced-order dynamic controllers to bound the system state trajectories below a specified threshold over a predefined finite time interval. Using the notion of dissipativity, we also ensure that the system is robust with respect to bounded external disturbances over the finite time interval. Sufficient conditions for the uncertain closed-loop system trajectories to simultaneously satisfy finite-time boundedness and dissipativity to external disturbances are given in terms of parameter-dependent differential matrix inequalities. Further, parameter-independent differential linear matrix inequality (DLMI) conditions are presented to design time-varying control gains. The proposed dissipativity-based approach is less conservative as it generalises the procedure of designing finite-time robust controllers, encompassing various disturbance attenuation performance criteria like passivity and finite L 2 -gain. The applicability of the proposed approach is demonstrated through numerical simulation examples.