Estimated State Feedback Research Articles

Trajectory Tracking of Stochastic Open Quantum Systems Based on Online Estimated State Feedback Control

AbstractAn online estimated state feedback control for trajectory tracking in stochastic open quantum systems is proposed in this paper, which is based on the Lyapunov‐based control method. By inducing the error between the controlled state, and the target state as the error state, the trajectory tracking problem of the quantum system is transformed into the error state transition control problem. The quantum state online estimation method QST‐OADM is applied to estimate the state of the error state system online, and the tracking control laws are designed by using the quantum Lyapunov stability theorem for driving the stochastic open quantum system from an arbitrary initial state to an arbitrary trajectory. The numerical simulation experiments and results analyses are given.

LPV interpolation modeling and modal-based pole placement control for ball screw drive with dynamic variations

This paper presents a linear parameter varying (LPV) interpolation modeling method and modal-based pole placement (PP) control strategy for the ball screw drive (BSD) with varying dynamics. The BSD is modeled as a global LPV model with position-load dependence by selecting position and load as scheduling variables. The global LPV model is obtained from local subspace closed-loop identification and LPV interpolation modeling. A modal-based global LPV model is obtained through the similarity transformation. Based on this model, a modal-based LPV PP control strategy is proposed to achieve various modal control. Specifically, a state feedback control structure with an LPV state observer is designed to realize online state estimation and real-time state feedback control of modal state variables which cannot be measured directly. The steady-state error is minimized by introducing an error state space (SS) model with the integral effects. Moreover, the stability of the closed-loop system is analyzed according to the controllable decomposition and principle of separation. It is experimentally demonstrated that the proposed modal-based LPV PP control strategy can effectively achieve precise tracking and outstanding robustness meantime.

Control of combustion distributions in compression-ignition engines using rate-constrained model predictive control with reference preview

To support the transition toward sustainable alternative fuels, advanced combustion control strategies can enable operation of compression-ignition engines with a wide range of fuels under challenging inlet conditions. This work presents a rate-constrained model predictive controller that uses state estimate feedback and integral tracking to control combustion phasing distributions by coordinating fuel injection timing with the power supplied to an electrically heated in-cylinder ignition assist device. The controller was validated in simulation using a statistical virtual engine that replicates both transient and steady-state stochastic combustion behavior. This virtual engine was tuned with data from experiments conducted at a low pressure-temperature inlet condition that induced highly variable combustion behavior akin to operating with a low cetane fuel. The controller achieves rapid tracking of combustion phasing step commands by supplying ignition assist power when needed to support fuel injection timing. All the while, it maintains closed-loop combustion variability at less than 6% higher than the open-loop system variability, and enforces ignition assist power range and rate constraints to reduce thermo-mechanical stress on the actuator. Furthermore, reference tracking is ensured even if combustion sensitivity to the ignition assist actuator deviates by as much as 83% from the controller’s internal model, without the need for retuning control parameters. Finally, the controller can coordinate actuators early and speed up tracking when a reference trajectory is previewed ahead of time, and its horizons can be tuned in a manner that maintains desirable control performance without compromising on computational tractability.

On observer compensator design for non-autonomous control semi-linear evolution equations

This paper investigates the Luenberger observer design problem for non-autonomous control semilinear evolution equations with disturbances in Banach spaces. Then, the practicalstabilization problem of the system is solved, yielding a compensator based on the Luenberger observer by using integral inequalities of the Gronwall type. Sufficient conditions of the controller and observer problem are satisfied, we show that the proposed controller with estimatedstate feedback from the proposed practical Luenberger observer will achieve global practical stabilization. We develop novel ideas and techniques, which present the further development of mathematical control theory. Furthermore, an example is given to show the applicability of our theoretical results.

Robust Control of Nonlinear Discrete Systems With Perturbations Based on Estimated State Feedback

Robust Control of Nonlinear Discrete Systems With Perturbations Based on Estimated State Feedback

Estimated-State Feedback Fuzzy Compensator Design via a Decentralized Approach for Nonlinear-State-Unmeasured Interconnected Descriptor Systems

This paper investigates the decentralized fuzzy control problems for nonlinear-state-unmeasured interconnected descriptor systems (IDSs) that utilize the observer-based-feedback approach and the proportional–derivative feedback control (PDFC) method. First of all, the IDS is represented as interconnected Takagi–Sugeno (T–S) fuzzy subsystems. These subsystems can effectively capture the dynamic behavior of the system through fuzzy rules. For the stability analysis of the system, this paper uses the free-weighing Lyapunov function (FWLF), which allows the designer to set the weight matrix, to achieve the desired control performance and design the controller more easily. Furthermore, the control problem can be transformed into a set of linear matrix inequalities (LMIs) through the Schur complement, which can be solved using convex optimization methods. Simulation results confirm the effectiveness of the proposed method in achieving the desired control objectives and ensuring system stability.

Robust fault estimation and proportional derivative fault tolerant control for a class of singular systems with interval time‐varying delay and disturbance

SummaryThis paper deals with observer‐based fault estimation (FE) and proportional derivative state feedback fault tolerant control (FTC) schemes for singular systems affected by actuator fault, interval time‐varying delay and external disturbance. Firstly, the system transformation method of constructing the derivative matrix into a full‐rank matrix is adopted to transform the singular system into a normal system, which effectively eliminates the impulse characteristic of the singular system. Secondly, in the design of the dynamic observer, fault estimation utilizes the real‐time output error and its derivative simultaneously, which can achieve better estimation performance when the fault change frequently. Most importantly, the observer‐based FTC adopts a proportional derivative state feedback control, considers disturbance and interval time‐varying delay, and the introduction of state estimation derivative term can eliminate the impulse property of the closed‐loop system, which optimizes the design scheme of the fault‐tolerant controller. The obtained sufficient conditions for stability can be solved by the strict linear matrix inequality (LMI), and the superiority of the conclusions will be further verified by the simulations.

Optimal Power Flow With State Estimation in the Loop for Distribution Networks

In this article, we propose a framework for running optimal control-estimation synthesis in distribution networks. Our approach combines a primal-dual gradient-based optimal power flow solver with a state estimation feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on certain online state measurements and noisy “pseudomeasurements.” We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least-squares estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudomeasurement variability and inherent sensor measurement noise.

Secure control scheme for CPSs under DoS attacks via multiple transmission channels and unknown input observer

The paper investigates the secure control problems for cyber–physical systems (CPSs) when the transmission channels suffer from Denial-of-Service (DoS) attacks based on switching observer and unknown input reconstruction (UIR). Firstly, an augmented system whose system state consists of the original system state and the measurement noises is set up, and the preconditions for the original system and augmented system are discussed in detail. Secondly, a full-order observer is constructed to generate the estimations of the augmented system state. Besides, based on the state estimation, an algebraic UIR method is developed and the UIR decouples the control input signal successfully. Thirdly, under the situation that some transmission channels suffer from DoS attacks, an observer-based secure controller is designed based on state estimation feedback and UIR feedback in view of a switching system. The stability of the switching system is analyzed as well. Finally, to verify the effectiveness of the proposed protocols, two simulation examples and the comparison with existing methods are given.

Distributed fault-tolerant control for heterogeneous multiagent systems and application in wireless power transfer grid

This paper investigates the incipient fault-tolerant problem of heterogeneous multiagent systems and applies the proposed method to the wireless power transfer grid. Firstly, a novel extended state observer is designed for every follower system, which not only relative output information of its agent but also contains output information of neighboring agents. Then, a state estimation feedback control scheme is proposed to compensate for the time delay and incipient faults effectively. It is worth noting that the proposed observer-based control strategy distributes the weight of the output information error. Therefore, the observer has higher adjustability and more substantial applicability. Further, we make a consistent analysis of the system under the proposed control scheme with the Lyapunov–Krasovskii theory that the sufficient conditions can be formed for the stability of the system. Finally, the validity of the proposed control scheme is demonstrated through numerical and application examples.

The Global Maximum Principle for Progressive Optimal Control of Partially Observed Forward-Backward Stochastic Systems with Random Jumps

This paper is concerned with a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enters into all the coefficients. In our model, the observation equation is not only driven by a Brownian motion but also a Poisson random measure, which also has correlated noises with the state equation. The partially observed global maximum principle is proved. To show its applications, a partially observed linear quadratic progressive optimal control problem of forward-backward stochastic differential equations with random jumps is investigated by the maximum principle and stochastic filtering. State estimate feedback representation of the optimal control is given in a more explicit form by introducing some ordinary differential equations.

Stabilization by an estimated state controller of nonlinear time-varying systems

Abstract In linear systems, it is well known that any combination of stabilizing state feedback controller and a state observer results in the output feedback controller which asymptotically stabilizes the closed-loop system. This is known as the separation principle, which does not generally hold for nonlinear systems. For nonlinear systems, the output feedback problem is usually pursued by extending the results of observer synthesis, which itself is a challenging problem. In this paper, we investigate the stabilization via an observer configuration problem for some classes of nonlinear time-varying systems by using new integral inequalities of Gronwall type. Given that the sufficient conditions of the controller and observer problem are satisfied, we show that the proposed controller with estimated state feedback from the proposed practical observer will achieve the global practical exponential stabilization. Furthermore, the effectiveness of the proposed scheme is shown through simulation for two numerical examples.

Model Predictive Control of Combustion Phasing in Compression Ignition Engines by Coordinating Fuel Injection Timing and Ignition Assist

Internal combustion engines may use ignition assisting heating elements such as glow plugs to facilitate combustion control in automotive or aircraft powertrains that operate with synthetic fuels of varying ignition behavior or at extreme inlet conditions. This work presents a model predictive controller (MPC) that regulates combustion phasing in compression ignition engines on a cycle-to-cycle basis by coordinating fuel start of injection (SOI) with power supplied to a glow plug acting as an ignition assist (IA) device, while enforcing IA actuator range and rate constraints. Simulations were conducted using a nonlinear virtual engine informed by data from a commercial engine operating at a condition that induced high combustion variability. A rate-based MPC formulation leveraging state estimate feedback and integral setpoint tracking was developed. Simulation results show the MPC scheme ensures steady-state tracking of combustion phasing within 70 engine cycles, conserves IA usage whenever possible to reduce thermo-mechanical stress on the actuator, and maintains closed-loop combustion variability at only 4% higher than the open-loop system variability. Furthermore, the controller maintains reference tracking even if combustion sensitivity to the actuators deviates by more than 20% from the controller's internal model, without the need for retuning control parameters.

A linear-quadratic partially observed Stackelberg stochastic differential game with application

This paper is concerned with a linear-quadratic partially observed Stackelberg stochastic differential game with correlated state and observation noises, where the control set is not necessarily convex. Both the leader and the follower have their own observation equations, and the information filtration available to the leader is contained in that available to the follower. Necessary and sufficient conditions of the Stackelberg equilibrium points are derived. In the follower’s problem, the state estimation feedback of optimal control can be represented by a forward-backward stochastic differential filtering equation and some Riccati equation. In the leader’s problem, via the innovation process, the state estimation feedback of optimal control is represented by a stochastic differential filtering equation, a semi-martingale process and three high-dimensional Riccati equations. As an application, a dynamic advertising problem with asymmetric information is studied, and the effectiveness and reasonability of the theoretical result are illustrated by numerical simulations.

Stackelberg stochastic differential game with asymmetric noisy observations

ABSTRACT This paper is concerned with a Stackelberg stochastic differential game with asymmetric noisy observation. In our model, the follower cannot observe the state process directly, but could observe a noisy observation process, while the leader can completely observe the state process. Open-loop Stackelberg equilibrium is considered. The follower first solve a stochastic optimal control problem with partial observation, the maximum principle and verification theorem are obtained. Then the leader turns to solve an optimal control problem for a conditional mean-field forward–backward stochastic differential equation, and both maximum principle and verification theorem are proved. A linear-quadratic Stackelberg stochastic differential game with asymmetric noisy observation is discussed to illustrate the theoretical results in this paper. With the aid of some new Riccati equations, the open-loop Stackelberg equilibrium admits its state estimate feedback representation. Finally, an application to the resource allocation and its numerical simulation are given to show the effectiveness of the proposed results.

A new actuator fault‐tolerant control for Lipschitz nonlinear system using adaptive sliding mode control strategy

AbstractThis article proposed a new adaptive integral sliding mode (ISM) based fault‐tolerant control (FTC) strategy to solve the actuator's faults and failures compensation problem for the class of Lipschitz nonlinear systems. A nominal state feedback virtual control law is designed first to stabilize the Lipschitz nonlinear system and to attain the desired nominal performance. To cater for the effect of faults and failures, the control allocation (CA) scheme reorganizes the virtual input signals among the healthy redundant actuators based on actuator's effectiveness level. Then, a nonlinear adaptive integral sliding mode controller (ISMC) is incorporated with the CA scheme to compensate for unknown disturbance and uncertainties effect that arises in the system by virtue of actuator faults/failures and error in fault estimation . An effective synthesis procedure is adopted to ensure the closed‐loop stability condition using linear matrix inequality (LMI) optimization. Finally, the FTC scheme is tested to achieve maneuvering control of coaxial octorotor unmanned aerial vehicle (UAV) system. Simulations are performed on the nonlinear system at different actuator faults/failures combinations. Moreover, the effect of wind‐gust, parameter variations, estimated state feedback and sensor noise are considered in nonlinear simulations. Finally, the results obtained during faults/failures are compared with the nominal condition and fixed ISMC based CA scheme.

Integrated sensor fault estimation and control for continuous-time switched systems: A new separation principle

In this paper, we address the state/fault estimation and observer-based control issues for switched systems with sensor faults. The main objective is to estimate sensor faults and compensate for their effects on the system state estimation, and then stabilize the switched system by the estimated state feedback. Applying the mode-dependent average dwell time (MDADT) concept and the Lyapunov stability theory, a new separation principle is developed, which allows formalizing the observer-based controller design in the form of linear matrix inequalities (LMI) instead of bilinear ones. Finally, a highly manoeuvrable aircraft technology (HiMAT) example, a DC–DC boost converter example, and a numerical example are investigated to show the practicability and efficiency of the obtained results.

A stackelberg game of backward stochastic differential equations with partial information

<p style='text-indent:20px;'>This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs) with partial information, where the information of the follower is a sub-<inline-formula><tex-math id="M1">\begin{document}$ \sigma $\end{document}</tex-math></inline-formula>-algebra of that of the leader. Necessary and sufficient conditions of the optimality for the follower and the leader are first given for the general problem, by the partial information stochastic maximum principles of BSDEs and forward-backward stochastic differential equations (FBSDEs), respectively. Then a linear-quadratic (LQ) Stackelberg game of BSDEs with partial information is investigated. The state estimate feedback representation for the optimal control of the follower is first given via two Riccati equations. Then the leader's problem is formulated as an optimal control problem of FBSDE. Four high-dimensional Riccati equations are introduced to represent the state estimate feedback for the optimal control of the leader. Theoretic results are applied to a pension fund management problem of two players in the financial market.</p>

Offset-free IMC with generalized disturbance models

Integral action is an essential component for offset-free response in many feedback control systems. Standard internal model control design rules ensure an offset-free response for open-loop stable plants. In this paper a linear feedback control structure is proposed that comprises an observer using an augmented plant model, state estimate feedback and disturbance estimate feedback. This allows internal model control design principles to be applied to unstable and marginally stable plants. Conditions are given for both nominal internal stability and offset-free action even in the case of plant-model mismatch. The Youla parameterization is recovered as a limiting case with reduced-order observers. The design is illustrated on a large scale non-square model with marginally stable dynamics.

Output Feedback Exponential Stabilization for a One-Dimensional Wave Equation With Control Matched Nonlinear Disturbance

In this article, we study the output feedback exponential stabilization of a one-dimensional wave equation with control matched nonlinear disturbance. The well posedness of the open-loop system, which is essentially important for the designs of observer and controller, is verified. By designing an infinite-dimensional unknown input state observer in place of the conventional extended state observer, we estimate the total disturbance in real time. Moreover, we prove the convergence of the disturbance estimator. Based on the disturbance estimator, we design a state observer by compensating the total disturbance, and an estimated state feedback controller to exponentially stabilize the original system by means of the Riesz basis approach. Some numerical simulations are presented.