Control Of Uncertain Systems Research Articles

On Robust Stability of Uncertain Control Systems With Time Delay: An Approach Based on the Overlap of Value Sets

On Robust Stability of Uncertain Control Systems With Time Delay: An Approach Based on the Overlap of Value Sets

Risk Assessment of Stealthy Attacks on Uncertain Control Systems

Risk Assessment of Stealthy Attacks on Uncertain Control Systems

On error-driven nonlinear ESO based control design with application to air–fuel ratio control of engines

In this paper, the tracking control problem of the uncertain control system is studied in the frame of uncertainties estimation and compensation. To eliminate the influence of external disturbances and internal uncertainties on the control system, the error-driven nonlinear extended state observer (EDN-ESO), whose gain is set as an increasing function with respect to the absolute value of estimation error of the system output, is proposed to improve the estimation performance for the “total disturbance”. Next, both the estimation error of proposed ESO and the tracking error of system output are proven to be bounded by selecting the lower bound and variation range of ESO’s bandwidth. Moreover, the convergence of the estimation error as well as the tracking error to zero is proven under certain conditions. Finally, the proposed design method is applied to the air–fuel ratio control system of gasoline engines, and the experimental results show that the proposed EDN-ESO can effectively adjust the observer gain, so as to enhance the tracking performance.

Reliability-constrained optimal attitude-vibration control for rigid-flexible coupling satellite using interval dimension-wise analysis

This study proposes an uncertain optimal attitude–vibration control method for rigid–flexible coupling satellites with reliability constraints based on the interval dimension-wise analysis. To model the complex uncertain control system, multi–source uncertainties in rigid–flexible coupling satellites are quantified to interval parameters. Based on the nominal rigid–flexible coupling satellite dynamic model, the interval attitude–vibration model is derived and the corresponding coupled state equation is established. Considering polynomial chaos expansions in the surrogate model, an interval dimension-wise analysis (IDWA) method is proposed to predict the uncertain state response of the uncertain attitude–vibration control system, which can help solve the overestimation problem of the conventional perturbation method. An interval linear quadratic regulator (LQR) is proposed by combining the IDWA method and deterministic LQR, to accurately optimize the uncertain control input and cost function. With regard to harsh deterministic state response constraints, this study proposes a non-probabilistic time-dependent reliability method, which allows for an effective evaluation by flexibly characterizing the relationship between the uncertain state response and threshold. The reliability-constrained multi–objective optimal attitude–vibration control problem can be solved by considering the nominal cost function and uncertain state response as two optimization objectives. The effectiveness of the proposed method is verified using a rigid–flexible coupling satellite.

Robust Model Predictive Control for Two-DOF Flexible-Joint Manipulator System

This paper presents a practical study on how to improve the ℋ∞ performance and meet the input–output constraints of the two-degrees-of-freedom (DOF) flexible-joint manipulator system (FJMS) with parameter uncertainties and external disturbances. For this reason, a robust constrained moving-horizon ℋ∞ controller is designed to improve the system ℋ∞ performance while still satisfying the input–output constraints of the uncertain system. First, the uncertain controlled system model of the two-DOF FJMS is established via the Lagrange equation method, Spong’s assumption, and the linear fractional transformation (LFT) technique. Then, the control requirements and input–output constraints of the uncertain system are transformed into the linear matrix inequality (LMI) via the theory of ℋ∞ control and the full-block multiplier technique. Next, the LMI optimization problem refreshed by the current state is addressed at each sample moment with the idea of the moving-horizon control of the model predictive control (MPC), and the calculated gain is implemented to the nonlinear closed-loop system under the state feedback structure. The validity and feasibility of the designed control scheme is finally verified via the results of simulation experiments.

Finite-time H∞ Control for Uncertain System With Time-varying Delay and Exogenous Disturbance

Finite-time H∞ Control for Uncertain System With Time-varying Delay and Exogenous Disturbance

Synthesis of adaptive gain robust model-following/tracking controllers for uncertain systems with multiple unknown dead-zone inputs via piecewise Lyapunov functions

ABSTRACT This paper considers a design problem of adaptive gain robust model-following/tracking controllers for a class of uncertain systems with multiple unknown dead-zone inputs via piecewise Lyapunov functions. The parameters for dead-zone characteristics are assumed to be unknown, and an adaptive dead-zone inverse method is applied so as to reduce the effect for dead-zone non-linearities. Moreover, for the purpose of reducing the effects of matched and mismatched uncertainties, compensation inputs are introduced. The proposed adaptive gain robust model-following/tracking controller can achieve that the tracking error asymptotically converges to zero. In this paper, by using piecewise Lyapunov functions, we show sufficient conditions for the existence of the proposed adaptive gain robust model-following/tracking controller. Finally, an example is given to demonstrate the effectiveness of the proposed controller design method.

Numerical over-approximation of invariance entropy via finite abstractions

For a closed-loop system with a digital channel between the sensor and controller, invariance entropy quantifies the smallest average rate of information above which a compact subset Q of the state set can be made invariant. There exist different versions of invariance entropy for deterministic and uncertain control systems, which are equivalent in the deterministic case. In this paper, we present the first numerical approaches to obtain rigorous upper bounds of these quantities. Our approaches are based on set-valued numerical analysis and graph-theoretic constructions. We combine existing algorithms from the literature to carry out our computations for several linear and nonlinear examples. A comparison with the theoretical values of the entropy shows that our bounds are of the same order of magnitude as the actual values.

Stabilization of Some Classes of Uncertain Control Systems with Evaluation of Admissible Disturbance for the Object Matrix

Stabilization of Some Classes of Uncertain Control Systems with Evaluation of Admissible Disturbance for the Object Matrix

Robust tracking composite nonlinear feedback controller design for time-delay uncertain systems in the presence of input saturation

In this study, a robust control technique is investigated for the reference tracking of uncertain time-delayed systems in the existence of the actuator saturation. Due to emerging of some control complexities, as well as the input limitations, time-varying delay, uncertainty, and external disturbance, such a tracking goal would be realized through suitable design of the composite nonlinear feedback (CNF) controller. Thus, considering the mentioned limitations, a Lyapunov-based procedure is used to determine the control law. Then, the parameters of the CNF input are derived by using the solution of a linear matrix inequality (LMI) problem. The planned tracking idea is numerically implemented in two uncertain control systems. Some performance characteristics (i.e., the tracking error, boundedness, and transient responses) are compared with similar ones. Accordingly, the simulations illustrate the efficiency of the suggested control procedure over the existing CNF approaches.

Stabilization of some classes of uncertain control systems with evaluation of admissible disturation for object matrix

Consider the system ̇x=M(·)x+enu,u=sTx, where M(·)∈Rn×n,s∈Rn, the pair (M·), enis uniformly controlable. The elements ofM(·)are nonlook-ahead functionals ofarbitrary nature. The object matrix is considering in form M(·) =A(·) +D(·), where A(·)has a form of globalized Frobenious matrix, D(·)is a matrix of disturbation. Consider thesquare Lyapunov functionV(x)with constant matrix of special form and number α >0 as estimate for ̇V for case D(·) = 0. The definition of such vectorsand such estimate ofnorm matrix D(·)that system is globally and exponentially stable are performed for every α >0.

Predictive extended state observer-based repetitive controller for uncertain systems with input delay

This article presents a predictive extended state observer-based repetitive controller (PESO-RC) to simultaneously track and reject periodic signals on systems with long input delay and parameter uncertainties. First, a novel extended state observer (ESO) is proposed to tackle periodic signals on processes with input delay. Then a simple low pass filter is incorporated and tuned to improve robustness against modelling errors. Moreover, the modified repetitive controller (MRC) is integrated to enhance the performance when compensating periodic signals without affecting the overall system’s stability. Stability criteria and robust stability analysis under modelling errors are studied to develop tuning guidelines. Furthermore, validation of the proposed controller and comparison studies are simulated in MATLAB and tested on a brushless DC servo motor which highlight the superior performance of PESO-RC.

Iterative approach for a class of fuzzy Volterra integral equations using block pulse functions

Fuzzy Integral equations is a mathematical tool for mod- eling the uncertain control system and economic. In this paper, we present numerical solution of nonlinear fuzzy Volterra integral equa- tions(NFVIEs) using successive approximations scheme and block-pulse functions. Additionally, the convergence analysis of the presented ap- proach is investigated involving Lipschitz and several conditions and error bound between the approximate and the exact solution is pro- vided. Finally, to approve the outcomes concerned with the theory a numerical experiment is considered.

A successive convex optimization method for bilinear matrix inequality problems and its application to static output‐feedback control

AbstractThis article explores a successive convex optimization method for solving a class of nonconvex programming problems subject to bilinear matrix inequality (BMI) constraints. In particular, many control issues can be boiled down to BMI problems, which are typically NP‐hard. To get out of the predicament, we propose a more relaxed feasible set to approximate the original one, based on which a local optimization algorithm is developed and its convergence is analyzed. As a case of application, we consider static output‐feedback control for uncertain systems with disturbances in restricted frequency intervals. In order to strengthen the disturbance‐rejection capability over the given frequency range, we establish sufficient and necessary analysis conditions via the generalized Kalman‐Yakubovich‐Popov lemma, under which the homogeneous polynomially parameter‐dependent technique is adopted to facilitate the design. Finally, several examples are given to demonstrate the efficiency of the results.

Unified control and detection framework and its applications: A review, some new results, and future perspectives

Initiated three decades ago, integrated design of controllers and fault detectors has continuously attracted research attention. The recent development of the unified control and detection framework with an observer-based residual generator in its core gives a more general form of the previous works. Its applications to residual centred modelling of uncertain control systems, fault detection in feedback control systems with uncertainties, fault-tolerant control (FTC) as well as control performance degradation monitoring, detection and recovery are introduced. In conclusion, some future perspectives are proposed.

Stability in measure for uncertain delay differential equations based on new Lipschitz conditions

Uncertain delay differential equations (UDDEs) charactered by Liu process can be employed to model an uncertain control system with a delay time. The stability of its solution always be a significant matter. At present, the stability in measure for UDDEs has been proposed and investigated based on the strong Lipschitz condition. In reality, the strong Lipschitz condition is so strictly and hardly applied to judge the stability in measure for UDDEs. For the sake of solving the above issue, the stability in measure based on new Lipschitz condition as a larger scale of applications is verified in this paper. In other words, if it satisfies the strong Lipschitz condition, it must satisfy the new Lipschitz conditions. Conversely, it may not be established. An example is provided to show that it is stable in measure based on the new Lipschitz conditions, but it becomes invalid based on the strong Lipschitz condition. Moreover, a special class of UDDEs is verified to be stable in measure without any limited condition. Besides, some examples are investigated in this paper.

Non-linear state feedback control for uncertain systems using a finite time disturbance observer

Non-linear state feedback control for uncertain systems using a finite time disturbance observer

Analysis of equivalent‐input‐disturbance‐based control systems and a coordinated design algorithm for uncertain systems

AbstractThe control method based on the equivalent‐input‐disturbance (EID) estimator and the Luenberger state observer has received much attention in recent years. However, the property of EID‐based control systems is still not well investigated. A number of design procedures were proposed but lacked sufficient theoretic justification. In this article, the two‐degree‐of‐freedom nature of an EID‐based control system is revealed. Specifically, the reference‐tracking is determined by an outer loop, while the disturbance rejection and robustness is determined by an inner loop consisting of the EID estimator and state observer. The bandwidth constraints on the inner loop are analyzed for plants having zeros or poles in the open right‐half plane by using the Bode and the Poisson integral formulas. These analyses provide a theoretic justification for conventional design procedures. Further, a coordinated design algorithm is provided for the EID‐based uncertain control systems. In addition, a comprehensive comparison of the EID‐based and the disturbance observer (DOB) based control systems is conducted in the system design aspect. Lastly, comparative studies of the EID‐based and DOB‐based control methods are given for various types of plants to validate the developed design algorithm.

Multiple model unfalsified adaptive generalized predictive control based on the quadratic inverse optimal control concept

AbstractUnfalsified adaptive control (UAC) is a class of switching control systems which deals with the control of uncertain systems. The UAC includes a bank of controllers, a supervisor, and a system in which the supervisor selects a stabilizing controller based on the system input and output data. Feasibility is the only assumption required in the UAC strategy, which guarantees that there is at least one stabilizing controller in the controller bank. UAC uses the cost detectability definition to prove closed‐loop stability. The combination of UAC and multiple model supervisory adaptive control (MMASC) results in the proposed unfalsified multi‐model control methodology that enjoys appropriate transient performance and stability proof with required minimum assumptions. In practical controller implementations, the effect of actuator constraints on the control signals is crucial. Despite the significance of constrained systems analysis in real applications, the input constraints in the structures of unfalsified control are not generally considered. Also, the stability analysis of constrained unfalsified control is key to its practical applications. In this article, the input constrained systems are considered using the constrained generalized predictive control (GPC) as the main controllers. Subsequently, to handle virtual signal generation for the GPCs in the UAC context, the inverse optimal control strategy is engaged and formulated to solve the signal generation problem. Simulation results are employed to show the effectiveness of the proposed methodology.

Stability-Based Controller Design of Cloud Control System With Uncertainties

A cloud control system (CCS) is inherently uncertain due to the dynamic services and resources in cloud computing. In this paper, an approach of modeling and controller design for CCS is proposed that considers the uncertainties existing in the controlled plant, network, and controller simultaneously; then, a general framework for modeling and controlling uncertain control systems is constructed. First, a typical CCS structure is presented, and the uncertainties in the CCS are analyzed and decomposed. On this basis, a generalized uncertain state-space model is established, which includes the interval controlled plant and the stochastic network, considering the time-delay and packet loss. Meanwhile, the cloud controller model with interval parameters and stochastic time-delay is designed, which includes the state observer and control law. Then, based on the Lyapunov stability theorem and the linear matrix inequality (LMI) method, a stability criterion for obtaining the parameters of the cloud controller is proposed, in which all the results are expressed in the form of the LMI. Finally, simulation results show the effectiveness and generalization performance of the designed cloud controller.