Terminal Weighting Matrix Research Articles

An active primary frequency regulation strategy for grid integrated wind farms based on model predictive control

The increasing penetration level of wind power can reduce the dependency on fossil fuels, but it is accompanied with challenges such as the jeopardized dynamic stability of the frequency of power grid. As an effective method to improve frequency dynamic stability, primary frequency regulation (PFR) is conventionally based on the feedback of measured frequency, by which means it is conducted through analyzing historical information. By taking the predictive information into account, this paper introduces an active PFR (APFR) strategy for grid integrated wind farms (WFs) to enhance control performance of PFR. According to small-signal models of power system integrated with WFs based on conventional PFR and APFR, the state-space predictive models are established to obtain the predictive states. Then, to take active measures to deal with the electrical load disturbance, the predicted frequency is optimized in a receding horizon period by adjusting the PFR power reference of WFs flexibly. Moreover, a finite terminal weighting matrix based Lyapunov​ function is presented to prove the asymptotic stability of the closed-loop model predictive control system. Finally, extensive case studies based on the standard test systems are performed to validate the effectiveness of the theoretical analysis and the superiority of APFR strategy.

Guidance for hypersonic re‐entry using receding horizon control with finite terminal weighting matrix

AbstractIn this article, nominal‐trajectory‐based guidance approach for hypersonic reentry vehicles is considered using the Vinh's equations. The nominal trajectory is generated via pseudo‐spectral method and then tracked by receding horizon control approach. Specially, several strategies are adopted to simplify the practical application. First, we formulate the receding optimal problem discretely using the approximated discrete linear state error dynamics. Thus, the differential matrix Riccati equation is substituted by a difference matrix Riccati equation. Second, we set the terminal state weighting matrix finite which brings flexibility of adjusting the sample period and prediction horizon. Third, the time‐varying state error dynamics is approximated by time invariant system. Lastly, instead of obtaining terminal weighting matrices which satisfy a linear matrix inequality using the LMI toolbox, we set them the same constant matrix. Naturally, numerical simulation is available to verify the validity and efficiency of the proposed approach.

Optimization and Simulation of DMC Algorithm with Terminal Weight Based on LQR Controller

Based on the multivariable dynamic matrix control algorithm, there are many similarities between the dynamic matrix control algorithm and LQR in the form of state equation, state variable and objective function. We can use the objective function of LQR to improve the objective function of DMC and improve the control effect of the system. Using the given mathematical model, the terminal weighting matrix of LQR is applied to DMC algorithm, and the optimized multivariable dynamic matrix control algorithm is simulated. The results show that the algorithm can effectively reduce the response time of the system, make the system sink faster and reach the given value faster.

Distributed RHC stabilization for discrete‐time large‐scale systems with imposed constraints

SummaryThis paper is concerned with finite horizon distributed stabilization of linear discrete‐time large‐scale systems with imposed constraints. Firstly, by constructing the performance index with two terminal weighted matrices, the necessary and sufficient conditions for stabilizing the system are derived. It is shown that distributed receding horizon control (RHC) can stabilize the discrete time large system with constraints if and only if two novel Lyapunov inequalities on the terminal weighting matrix are satisfied. Secondly, the finite horizon optimal control problem is solved by using the maximum principle (necessary condition), and the Riccati equation satisfying the corresponding distributed control system is derived. Based on the Riccati equation, the explicit optimal distributed RHC controller is obtained. Finally, simulation examples are used to verify the feasibility of distributed RHC to stabilize the system.

Towards improving constrained robust model predictive control with free control moves

An existing robust model predictive control (RMPC) algorithm parameterises the infinite horizon control moves into a set of free control moves over a fixed horizon and a state feedback law in the terminal region. This paper is towards further improving the feasibility and optimality of this kind of RMPC. The improvement is by introducing an extended parameter-dependent Lyapunov function to substitute the original parameter-dependent Lyapunov function. Correspondingly, the terminal-weighting matrix is extended parameter-dependent, the local control law is a non-parallel distributed compensation, and the terminal constraint set is an intersection of more ellipsoids. The new technique is demonstrated by a simulation example.

On stabilization of Itô stochastic time-varying systems

The stabilization with receding horizon control (RHC) of Ito stochastic time-varying systems is studied in this paper. Based on monotonically non-increasing of optimal cost and stochastic Lyapunov stability theory, a necessary and sufficient stabilization condition on the terminal weighting matrix is proposed, which guarantees the mean-square stability of the closed-loop system. The explicit receding horizon controller is obtained by employing stochastic maximum principle. Simulations demonstrate the effectiveness of the proposed method.

Robust model predictive control of constrained non‐linear systems: adopting the non‐squared integrand objective function

This study presents a novel robust model predictive control (MPC) method for constrained non-linear systems with control constraints and external disturbances. The control signal is obtained by optimising an objective function consisting of two terms: an integral non-squared stage cost and a non-squared terminal cost. The terminal weighting matrix is designed appropriately such that: (i) the terminal cost serves as a control Lyapunov function; and (ii) the resultant finite horizon cost can be treated as a quasi-infinite horizon cost. Provided that the Jacobian linearisation of the system to be controlled is stabilisable and the optimisation is initially feasible, sufficient conditions ensuring the recursive feasibility of the optimisation and the robust stability of the closed-loop system are established. It is shown that the conditions rely on an appropriate design of the sampling interval with respect to a certain given disturbance level. The effectiveness of the proposed method is illustrated through a numerical example.

Receding horizon disturbance attenuation for Takagi–Sugeno fuzzy switched dynamic neural networks

In this paper, we propose a new receding horizon disturbance attenuator (RHDA) for Takagi–Sugeno (T–S) fuzzy switched Hopfield neural networks with external disturbance. First, a new set of linear matrix inequality (LMI) conditions is proposed for the finite terminal weighting matrix of the receding horizon cost function with a cross term. Second, under this condition, we show that the proposed RHDA attenuates the effect of external disturbance on T–S fuzzy switched Hopfield neural networks with a guaranteed infinite horizon H∞ performance. In addition, we prove that the proposed RHDA guarantees internal stability in closed-loop systems. A numerical example is presented to describe the effectiveness of the proposed RHDA scheme.

Receding Horizon Robust Control for Nonlinear Systems Based on Linear Differential Inclusion of Neural Networks

In this paper, we present a new receding horizon neural robust control scheme for a class of nonlinear systems based on the linear differential inclusion (LDI) representation of neural networks. First, we propose a linear matrix inequality (LMI) condition on the terminal weighting matrix for a receding horizon neural robust control scheme. This condition guarantees the nonincreasing monotonicity of the saddle point value of the finite horizon dynamic game. We then propose a receding horizon neural robust control scheme for nonlinear systems, which ensures the infinite horizon robust performance and the internal stability of closed-loop systems. Since the proposed control scheme can effectively deal with input and state constraints in an optimization problem, it does not cause the instability problem or give the poor performance associated with the existing neural robust control schemes.

Model predictive stabilizer for T–S fuzzy recurrent multilayer neural network models with general terminal weighting matrix

This paper investigates the model predictive stabilization problem for Takagi–Sugeno (T–S) fuzzy multilayer neural networks with general terminal weighting matrix. A new set of linear matrix inequality (LMI) conditions on the general terminal weighting matrix of receding horizon cost function is presented such that T–S fuzzy multilayer neural networks with model predictive stabilizer are asymptotically stable. The general terminal weighting matrix of receding horizon cost function can be obtained by solving a set of LMIs. A numerical example is given to illustrate the effectiveness of the proposed stabilization scheme.

Takagi–Sugeno fuzzy receding horizon [formula omitted] chaotic synchronization and its application to the Lorenz system

In this article, we propose a new H∞ synchronization method for chaotic systems with external disturbance based on the Takagi–Sugeno (T–S) fuzzy model and receding horizon control. This synchronization method is called a Takagi–Sugeno fuzzy receding horizon H∞ synchronization (TSFRHHS) method. A new set of matrix inequality conditions on the terminal weighting matrix is proposed for T–S fuzzy chaotic systems wherein non-increasing monotonicity of the optimal cost is guaranteed. Under this set of terminal inequality conditions, the proposed TSFRHHS method guarantees the infinite horizon H∞ performance for T–S fuzzy chaotic systems with external disturbance. As an application of the proposed synchronization method, the TSFRHHS problem for the Lorenz system is investigated.

Output Feedback Model Predictive Tracking Control Using a Slope Bounded Nonlinear Model

In this paper, an output feedback model predictive tracking control method is proposed for constrained nonlinear systems, which are described by a slope bounded model. In order to solve the problem, we consider the finite horizon cost function for an off-set free tracking control of the system. For reference tracking, the steady state is calculated by solving by quadratic programming and a nonlinear estimator is designed to predict the state from output measurements. The optimized control input sequences are obtained by minimizing the upper bound of the cost function with a terminal weighting matrix. The cost monotonicity guarantees that tracking and estimation errors go to zero. The proposed control law can easily be obtained by solving a convex optimization problem satisfying several linear matrix inequalities. In order to show the effectiveness of the proposed method, a novel slope bounded nonlinear model-based predictive control method is applied to the set-point tracking problem of solid oxide fuel cell systems. Simulations are also given to demonstrate the tracking performance of the proposed method.

Receding horizon H<inf>∞</inf> control for discrete-time Markovian jump linear systems

Receding horizon H ∞ control scheme which can deal with both the H ∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin's minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality (LMI) form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

Network-based predictive control of multirate systems

This study investigates the problem of model predictive control (MPC) for networked multirate control systems (NMCSs) with the output sampling period several times larger than the input updating period. Both sensor-to-controller and controller-to-actuator network-induced delays are considered and are assumed to be upperbounded by one output sampling period. Firstly, using a modified multirate MPC scheme, where the future control sequence is used to compensate for the network-induced time delays, the closed-loop NMCSs are described as switched systems. Sufficient stability conditions are established via a switched Lyapunov function approach. Then, a controller design method for stabilising NMCSs is proposed based on a finite input and state horizon cost with a finite terminal weighting matrix. The feedback gain matrix dependent of every sampling output can be obtained by solving linear matrix inequalities (LMIs). Finally, examples are provided to show the effectiveness of the proposed method.

RECEDING HORIZON H∞ CONTROL FOR SYSTEMS WITH A STATE-DELAY

This paper proposes the receding horizon H∞ control (RHHC) for linear systems with a state-delay. We first proposes a new cost function for a finite horizon dynamic game problem. The proposed cost function includes two terminal weighting terms, each of which is parameterized by a positive definite matrix, called a terminal weighting matrix. Secondly, we derive the RHHC from the solution to the finite dynamic game problem. Thirdly, we propose an LMI condition under which the saddle point value satisfies the nonincreasing monotonicity. Finally, we show the asymptotic stability and H∞-norm boundedness of the closed-loop system controlled by the proposed RHHC. Through a numerical example, we show that the proposed RHHC is stabilizing and satisfies the infinite horizon H∞-norm bound.

Model predictive control: Terminal region and terminal weighting matrix

Many efforts have been made for model predictive control MPC to enlarge terminal region where the stability is guaranteed by including a proper terminal weighting. This paper investigates how to maximize the ellipsoidal terminal region by using a more general method to design MPC: calculating terminal region and terminal weighting separately. With Jordan canonical form, the new ellipsoid-based method can result in terminal regions which are infinite (in certain directions) even in the case of open-loop unstable systems. Some most popular methods are just special cases of this new method. Simulation results illustrate the effectiveness of the proposed algorithms.

RHC를 기반으로 하는 열간압연 루퍼 제어

In this paper, a new looper controller is proposed to minimize the tension variation of a strip in the hot strip finishing mill. The proposed control technology is based on a receding horizon control (RHC) to satisfy the constraints on the control input/state variables. The finite terminal weighting matrix is used instead of the terminal equality constraint. The closed loop stability of the RHC for the looper system is analyzed to guarantee the monotonicity of the optimal cost. Furthermore, the RHC is combined with a 4SID(Subspace-based State Space System Identification) model identifier to improve the robustness for the parameter variation and the disturbance of an actuator. As a result, it is shown through a computer simulation that the proposed control scheme satisfies the given constraints on the control inputs and states: roll speed, looper current, unit tension, and looper angle. The control scheme also diminishes the tension variation for the parameter variation and the disturbance as well.

Robust constrained predictive control using a sector bounded nonlinear model

Robust model predictive control technique is proposed for constrained nonlinear systems are modelled as systems with sector-bounded nonlinearities. The controller design problem is formulated as a minimisation of the upper bound of a finite-horizon cost function subject to cost monotonicity. For cost monotonicity, a linear matrix inequality (LMI) condition for terminal inequality is derived using a parameter-dependent terminal weighting matrix. The optimisation problem that satisfies the terminal inequality is solved by semidefinite programming involving LMIs. Numerical examples are included to illustrate the effectiveness of the proposed method.

Stability-Guaranteed Horizon Size for Receding Horizon Control

We propose a stability-guaranteed horizon size (SgHS) for stabilizing receding horizon control (RHC). It is shown that the proposed SgHS can be represented explicitly in terms of the known parameters of the given system model and is independent of the terminal weighting matrix in the cost function. The proposed SgHS is validated via a numerical example.

Robust model predictive control for norm-bounded uncertain systems using new parameter dependent terminal weighting matrix

A new robust model predictive control (MPC) technique is proposed for norm-bounded uncertain systems with input constraints. In order to improve feasibility and system performance, we propose an LMI condition for the cost monotonicity by using a new parameter dependent terminal weighting matrix. We formulate the problem as a minimization of the upper bound of infinite horizon cost function subject to the LMI condition for the cost monotonicity. A numerical example shows the effectiveness of the proposed method.