Problem Of Output Stabilization Research Articles

Predictive observer–based control for lower triangular time-delay systems subject to mismatched disturbances

This paper develops a predictive observer–based control (PO-BC) scheme to address the output stabilization problem of a class of time-delay systems subject to mismatched complex disturbances. Initially, a novel predictive observer is proposed to anticipate future information related to both disturbances and system states. By integrating these predictions, a composite controller is constructed, comprising feedback and feedforward compensation. A systematic approach for selecting control parameters is presented to facilitate easy implementation. The theoretical analysis demonstrates that as long as appropriate parameters are selected, the predictive observer can accurately predict both disturbances and system states, and the system’s output can asymptotically converge to zero. Finally, the effectiveness of the proposed scheme is validated through sufficient simulations.

Static output feedback control for positive 2D discrete systems in Roesser model

Abstract This paper investigates the output stabilization problem for multi-input multi-output positive 2D systems described by a linear discrete-time Roesser system. This kind of systems have the property that the horizontal and vertical states take non-negative values whenever the initial boundaries are non-negative. Conditions for the existence of desired static output feedback controllers guaranteeing the resultant closed-loop system to be positive and asymptotically stable are obtained. Also, the synthesis of static output feedback controllers, including the requirement of positivity of the controllers, is solved. These results are then extended to the case of uncertain plants. All of the proposed conditions are expressed in terms of Linear Programming, which can be easily verified by using standard numerical software. Finally, several numerical examples are included to illustrate the validity and the effectiveness of the developed results.

On the Output Stabilization Problem: Constructing a Delay Feedback for a Chain of Integrators

On the Output Stabilization Problem: Constructing a Delay Feedback for a Chain of Integrators

Output stabilization of strongly minimum-phase multivariable nonlinear systems

This paper addresses the problem of output stabilization of invertible MIMO nonlinear systems. A unifying procedure is presented, that consists in the preliminary use of a statefeedback to induce an upper triangular structure. Assuming that the upper subsystem in this structure is input-to-state stable (to a compact invariant set), the output stabilization problem is reduced to the problem of globally asymptotically stabilizing the lower subsystem.

Dynamic output stabilization of control systems: An unobservable kinematic drone model

The problem of dynamic output stabilization is a very general and important problem in control theory. This problem is completely solved in the case where the system under consideration is uniformly observable. However, usually, nonlinear systems do not share this property: in general, systems are observable or not depending upon the control as a function of time. In this general situation, very little is known about dynamic output stabilization.In this paper, we solve the problem for a classical academic kinematic model for drones whose observability properties are especially bad.

Separation principle for quasi‐one‐sided Lipschitz nonlinear systems with time delay

SummaryIn this article, we address the problem of output stabilization for a class of nonlinear time‐delay systems. First, an observer is designed for estimating the state of nonlinear time‐delay systems by means of quasi‐one‐sided Lipschitz condition, which is less conservative than the one‐sided Lipschitz condition. Then, a state feedback controller is designed to stabilize the nonlinear systems in terms of weak quasi‐one‐sided Lipschitz condition. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the observer‐based controller. Under the quasi‐one‐sided Lipschitz condition, state observer and feedback controller can be designed separately even though the parameter (A,C) of nonlinear time‐delay systems is not detectable and parameter (A,B) is not stabilizable. Finally, a numerical example is provided to verify the efficiency of the main results.

A modified sliding mode control of a nonlinear methane fermentation process

A continuous methane fermentation process for biogas production is considered. This biogas production process is described by a system of two nonlinear differential equations and one nonlinear algebraic equation. The paper purpose is to propose an approach for designing a modified sliding mode control (so-called binary control) of a nonlinear methane fermentation process. The control design is carried out with direct use of nonlinear model and on-line measurement for two variables only (the concentration of the organic pollutants and biogas production rate). The model of the sliding mode control is developed with respect to an auxiliary input variable in order to obtain the smooth signal of the dilution rate, which is need in the fermentation processes. The state variables, external disturbance, process output and control input are varied in the known intervals. The asymptotic output stabilization problem is solved. The good system robustness with the designed modified sliding mode control (the binary control) about various disturbances is proved through simulation investigations inMATLABusingSimulink.

Riemann Liouville Fractional Spatial Derivative Stabilization of Bilinear Distributed Systems

The goal of this paper is to study a fractional output stabilization problem: the stabilization of the state fractional spatial derivative of complex purely imaginary order i α with α ∈]0,1[, for bilinear distributed systems. Firstly, we develop sufficient conditions for exponential, strong and weak fractional output stabilization for the considered system, also, we offer some examples illustrating the obtained results. Moreover, we characterise the stabilizing control which minimizes an appropriate cost. Finally, an illustrating example with numerical simulations is given.

Distributed optimization for a class of high‐order nonlinear multiagent systems with unknown dynamics

SummaryIn this paper, we study a distributed optimization problem for a class of high‐order multiagent systems with unknown dynamics. In comparison with existing results for integrators or linear agents, we need to overcome the difficulties brought by the unknown nonlinearities and the optimization requirement. For this purpose, we employ an embedded control‐based design and first convert this problem into an output stabilization problem. Then, two kinds of adaptive controllers are given for these agents to drive their outputs to the global optimal solution under some mild conditions. Finally, we show that the estimated parameter vector converges to the true parameter vector under some well‐known persistence of excitation condition. The efficacy of these algorithms was verified by a simulation example.

Global finite‐time output stabilization of nonlinear systems with unknown measurement sensitivity

SummaryThis paper focuses on the output stabilization problem for a class of strict‐feedback systems with unknown nonlinear dynamics and unknown measurement sensitivity. The imprecise sensor measurements render the existing robust control approaches such as neuro or fuzzy control infeasible. A solution is provided in this paper by a feat of the concept of tuning functions and barrier Lyapunov functions (BLFs). Utilizing the modification capability of tuning functions, global stability is preserved. Exploiting the potential robustness of BLFs, the effect of unmodeled dynamics is counteracted under sensitivity errors. The combination of tuning functions with BLFs further leads to a distinct property that the real system output converges to an adjustable region in finite time. Compared with the existing results, the need for prior knowledge of system nonlinearities and measurement sensitivity is removed in this paper. Finally, simulation results illustrate the established theoretical findings.

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

SummaryThe problem of output stabilization and disturbance rejection for input‐delayed systems is tackled in this work. First, a suitable transformation is introduced to translate mismatched disturbances into an equivalent input disturbance. Then, an extended state observer is combined with a predictive observer structure to obtain a future estimation of both the state and the disturbance. A disturbance model is assumed to be known but attenuation of unmodeled components is also considered. The stabilization is proved via Lyapunov‐Krasovskii functionals, leading to sufficient conditions in terms of linear matrix inequalities for the closed‐loop analysis and parameter tuning. The proposed strategy is illustrated through a numerical example.

Output Regulation for a Class of Parameter Uncertain Systems

The problem of robust output regulation is studied for a class of parameter uncertain systems under unity output feedback control. The objective is tracking of the desired reference trajectory in the presence of the disturbance, both generated by a common exosystem. Because of the anti-stability of the exosystem and potentially unbounded reference trajectory, the output tracking error is employed as the measurement signal and used as the input to the feedback controller. The method of p-copy of the internal model is utilized to augment the plant dynamics. Assuming that the output regulation condition is satisfied for all the parameter uncertainties, it is shown that the problem of robust output regulation is equivalent to the problem of robust output stabilization. Furthermore for quadratically bounded parameter uncertainties, an application of the notion of the quadratic stability leads to H∞ based robust control, and the maximum allowable uncertainty bound can be computed, below which the robust output regulation can be achieved.

Interval Observer Approach to Output Stabilization of Linear Impulsive Systems

The problem of output stabilization is studied for a class of linear hybrid systems subject to signal uncertainties: linear impulsive systems under dwell-time constraints. Two problems are considered. First, an interval observer estimating the set of admissible values for the state is designed. Next, an output stabilizing feedback design problem is studied where the stability is checked using linear matrix inequalities (LMIs). To the best of our knowledge, interval observer approach has never been proposed for the stabilization of this class of hybrid systems. Efficiency of the proposed approach is demonstrated by computer experiments for Fault Detection and Isolation (FDI) and Fault-Tolerant Control (FTC) of a power split device with clutch for heavy-duty military vehicles.

Decentralized bounded input bounded output stabilization of perturbed interconnected time-delay power systems with energy storages

This paper presents a new decentralized bounded input bounded output (BIBO) stabilization problem for a class of interconnected time-delay systems and its application to power systems with energy storages. We first provide conditions for the derivation of an ellipsoid that bounds a given linear functions of the state vector. Then, a design procedure is proposed to synthesize decentralized static output feedback controllers. The designed controllers guarantee that a given linear functions of the state vector, starting from any initial condition, converges exponentially to its prescribed zones. To deal with the time-delay issue, we use an improved weighted integral inequality recently reported in the literature to derive less conservative exponential stability conditions. Then, our presented control approach is applied to an interconnected power system integrated energy storages with multiple time delays. We synthesis decentralized static output feedback load frequency controllers to guarantee that the system frequency and interchanged power converge to their prescribed zones exponentially from any initial conditions. The controller’s construction is simpler and easier for implementation due to only the local output measurements are required. In order to systematically obtain the controller gains, an effective procedure using linear matrix inequality based stabilisation criteria, which can be solved by various computation tools, is provided. Finally, the effectiveness of the proposed control scheme is verified by comprehensive simulations.

Stabilization of Takagi–Sugeno models with non-measured premises: Input-to-state stability approach

This work deals with the observer-based output stabilization problem for Takagi–Sugeno models with non-measured premises. It aims at providing efficient design methods for the controller/observer pair with minimal constrained hypothesis on the model non-linear functions. The main idea is to consider the closed loop and the error dynamic as two interacting subsystems and study them in the Input to State Stability framework. This paper provides also some results about the existence of a stabilizing output feedback for all models of a sub-class of Takagi–Sugeno models. To illustrate the efficiency of the proposed design procedures, illustrative examples and a comparative study with existing results in the literature based on more restrictive hypothesis are presented.

Adaptive fault tolerant control for a class of multi‐input multi‐output nonlinear systems with both sensor and actuator faults

SummaryCompared with the fault diagnosis, detection, and isolation literature, very few results are available to discuss control algorithms directly for multi‐input multi‐output nonlinear systems with both sensor and actuator faults in the fault tolerant control literature. In this work, we present a fault tolerant control algorithm to address the system output stabilization problem for a class of multi‐input multi‐output nonlinear systems with both parametric and nonparametric uncertainties, subject to sensor and actuator faults that can be both multiplicative and additive. All elements of the sensor measurements and actuator components can be faulty. Besides, the control input gain function is not fully known. Backstepping method is used in the analysis and control design. We show that under the proposed control scheme, uniformly ultimate boundedness of the system output is guaranteed, while all closed‐loop system signals stay bounded. In the cases where the sensor faults are only multiplicative, exponential convergence of the system state variables into small neighbourhoods around zero is guaranteed. An illustrative example on a robot manipulator model is presented in the end to further demonstrate the effectiveness of the proposed control scheme.

Stabilization of stationary affine control systems with discrete time

We obtain new sufficient conditions for the local and global asymptotic stabilization of the zero solution of a nonlinear affine control system with discrete time and with constant coefficients by a continuous state feedback. We assume that the zero solution of the free system is Lyapunov stable. For systems with linear drift, we construct a bounded control in the problem of global asymptotic state and output stabilization. Corollaries for bilinear systems are obtained.

On the stabilization of switchable linear systems

We consider output and state stabilization problems for switchable linear systems under various assumptions on the switching rules. For the solution of these problems, we suggest to use the simultaneous stabilization method.

Sufficient conditions for the stabilization of linear dynamical systems

We consider the output stabilization problem for a linear time-independent system. We show that if the system output is zero, y(t) ≡ 0, then, for the stabilization of the entire state vector, the sufficient condition of stability of the zero dynamics can be replaced by the boundedness of the system input (provided that the characteristic polynomial of the zero dynamics has no eigenvalues on the imaginary axis).

Output stabilization for a class of nonlinear systems via high-gain observer with limited gain power

We address the problem of output stabilization for the class of nonlinear minimumphase systems with a well-defined relative degree whose output is affected by measurement noise. In the proposed control structure the derivatives of the output are estimated by means of a new high-gain observer proposed in Astolfi and Marconi [2015], which, with respect to high-gain observers conventionally used in literature, has limited gain power. The advantage in using the proposed observer is in its implementation for systems with high relative degree and in the sensitivity to the sensor noise. Simulation results are presented to show the effectiveness of the proposed control structure.