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1.
This paper presents solution of the optimal linear-quadratic controller problem for unobservable integral Volterra systems with continuous/discontinuous states under deterministic uncertainties, over continuous/discontinuous observations. Due to the separation principle for integral systems, the initial continuous problem is split into the optimal minmax filtering problem for integral Volterra systems with deterministic uncertainties over continuous/discontinuous observations and the optimal linear-quadratic control (regulator) problem for observable deterministic integral Volterra systems with continuous/discontinuous states. As a result, the system of the optimal controller equations are obtained, including the linear equation for the optimally controlled minmax estimate and two Riccati equations for its ellipsoid matrix (optimal gain matrix of the filter) and the optimal regulator gain matrix. Then, in the discontinuous problems, the equation for the optimal controller and the equations for the optimal filter and regulator gain matrices are obtained using the filtering procedure for deriving the filtering equations over discontinuous observations proceeding from the known filtering equations over continuous ones and the dual results in the optimal control problem for integral systems. The technical example illustrating application of the obtained results is finally given.  相似文献   

2.
We study in this paper solutions to several kinds of linear bimatrix equations arising from pole assignment and stability analysis of complex-valued linear systems, which have several potential applications in control theory, particularly, can be used to model second-order linear systems in a very dense manner. These linear bimatrix equations include generalized Sylvester bimatrix equations, Sylvester bimatrix equations, Stein bimatrix equations, and Lyapunov bimatrix equations. Complete and explicit solutions are provided in terms of the bimatrices that are coefficients of the equations/systems. The obtained solutions are then used to solve the full state feedback pole assignment problem for complex-valued linear system. For a special case of complex-valued linear systems, the so-called antilinear system, the solutions are also used to solve the so-called anti-preserving (the closed-loop system is still an antilinear system) and normalization (the closed-loop system is a normal linear system) problems. Second-order linear systems, particularly, the spacecraft rendezvous control system, are used to demonstrate the obtained theoretical results.  相似文献   

3.
This paper will present new theoretical and applied solutions for intelligent data analysis and information management in the fields of cognitive economics. Intelligent data analysis and information management are performed by information systems called cognitive systems, dedicated for semantic interpretation of acquired business information. To interpret the meaning of the analysed data, complex linguistic algorithms must be used, based on which it is possible to find the core information elements for business processes forecasting and economical knowledge management. The presentation of selected methods of semantic data analysis in cognitive economy, which allow to perform both local and global information management forms the main subject of this paper. Here, semantic analysis methods are dedicated to cognitive economics problems, namely the interpretation, analysis and assessment of the meaning of selected sets of economic/financial ratios. The meaning of the interpreted data sets is assessed by analysing the layers of meaning contained in data analysed sets. Obtained semantic information may be used in future business processes evaluation and forecasting.  相似文献   

4.
This paper is concerned with the output regulation problem of matrix second order singular systems via measurement output feedback. It is shown that the solvability of output regulation problem of matrix second order singular systems is equivalent to the solvability of a set of matrix equations, which are called regulator equations. The solvability condition and solutions of the regulator equations are given, which can be used to solve the output regulation problem. A numerical example is provided to demonstrate the effectiveness of the proposed method.  相似文献   

5.
Stability notions and Lyapunov functions for sliding mode control systems   总被引：2，自引：0，他引：2  
The paper surveys mathematical tools required for stability and convergence analysis of modern sliding mode control systems. Elements of Filippov theory of differential equations with discontinuous right-hand sides and its recent extensions are discussed. Stability notions (from Lyapunov stability (1982) to fixed-time stability (2012)) are observed. Concepts of generalized derivatives and non-smooth Lyapunov functions are considered. The generalized Lyapunov theorems for stability analysis and convergence time estimation are presented and supported by examples from sliding mode control theory.  相似文献   

6.
In this paper, we consider an initial value problem for linear matrix coefficient systems of the fractional-order neutral differential equations with two incommensurate constant delays in Caputo’s sense. Firstly, we introduce the exact analytical representation of solutions to linear homogeneous and non-homogeneous neutral fractional-order differential-difference equations system by means of newly defined delayed Mittag–Leffler type matrix functions. Secondly, a criterion on the positivity of a class of fractional-order linear homogeneous time-delay systems has been proposed. Furthermore, we prove the global existence and uniqueness of solutions to non-linear fractional neutral delay differential equations system using the contraction mapping principle in a weighted space of continuous functions with regard to classical Mittag–Leffler functions. In addition, Ulam–Hyers stability results of solutions are attained based on fixed-point approach. Finally, we present an example to demonstrate the applicability of our theoretical results.  相似文献   

7.
This paper considers the tracking control problem for nonlinear Markov jump systems based on T–S fuzzy model approach with incomplete mode information. It is assumed that the mode transition rate matrix is not a priori knowledge and only partial information is available. Moreover, the mode where the system stays when operating is not fully accessible to the designed controller. In this incomplete mode information scenario, a hidden Markov model based mechanism is modified to simulate the mode deficiency mapping. The incomplete transition rate matrix is well defined in the form of a polynomial. Based on this, by constructing a polynomially parameter-dependent Lyapunov matrices and linear matrix techniques, sufficient conditions are established to ensure the stochastic stability and a prescribed tracking performance. The controller design scheme are presented by solving a series of LMIs. Examples are given in the end to illustrate the effectiveness of our proposed results.  相似文献   

8.
There is a strong analogy between mechanical structural elements and magnetic circuit components which can be extended to include hysteretic energy losses associated with yielding in mechanical systems and saturation in magnetic components. Procedures for developing finite state models of hysteretic components are presented using a small number of basic elements. Using bond graph techniques, it is shown that, when dual structural models are used, elements may be assembled in arbitrary numbers to achieve any desired accuracy without problems of derivative causality. The reason for the dual structure can be seen from physical reasoning. The shape of the hysteresis curve for magnetic materials generally requires more elements for a given degree of approximation than the shape of the typical mechanical hysteresis curve.  相似文献   

9.
This paper is concerned with Markovian jump systems subject to incomplete knowledge of transition probabilities and actuator saturation. The system under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities. By introducing some free-connection weighting matrices to handle the inaccessible elements of transition probabilities, a new criterion is established to guarantee the stochastic stability of the closed-loop system. An optimization problem with LMI constraints is then formulated to determine the largest contractively invariant set in mean square sense. Finally, two numerical examples are provided to illustrate the merits of our method.  相似文献   

10.
Dynamic systems containing particles and rigid bodies capable of movement in two- or three-dimensions may be represented by equations of motion in several basic forms. In all cases geometric nonlinearities are involved and terms arise in the equations which are difficult to understand and interpret. The equations often conceal the basic structure of the dynamic model of the system since only combinations of parameters and combined effects of various constraints finally appear.In this paper the basic relations for the dynamic elements as well as the transformations among internal forces and velocities are depicted using bond graphs. The energetic structure of the system is thus exhibited in multiport form. This aids in the exploration of alternative equation formulation and in understanding of the assumptions involved in any particular equation set. Further, a bond graph model is easily coupled with nonmechanical dynamic models through force or motion generators.  相似文献   

11.
Starting from one-dimensional nonlinear advecting equations, this paper has probed the energy properlies of discontinuous solutions, investigated that it is suitable to adopt energy decaying scheme to compute discontinuous solutions, compared and testified several difference schemes with dissipation effects, pointed out that it is easy to bring about nonlinear stabilities in doing discontinuous computation, and listed several better-effect schemes.  相似文献   

12.
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13.
《Journal of The Franklin Institute》2023,360(13):10365-10385
This paper investigates a spatiotemporal sampled-data fuzzy control strategy for switched singularly perturbed partial differential equation (PDE) systems, where the systems’ operation modes obey average dwell-time switching mechanism. To efficiently deal with nonlinear terms and guarantee the system stability for the considered systems, a spatiotemporal sampled-data fuzzy control scheme is developed. Furthermore, based on the fact that mode mismatch phenomena during switching and sampling, through formulating novel Lyapunov functionals (LFs) with the discontinuous terms and mode-dependent two-sided looped-functionals, which can fully utilize the state information of the sampling period, a new exponential stability criterion is provided for the target systems. Finally, an example is provided to prove the validity of the proposed control approach.  相似文献   

14.
This paper investigates the issue of finite/fixed-time bipartite consensus (FFTBC) of multi-agent systems with signed graphs. A new unified framework of finite-time and fixed-time bipartite consensus is built via some discontinuous control protocols based on the theory of differential inclusion and set-valued Lie derivative. Under the structurally balanced or unbalanced signed graphs, the goal of FFTBC is reached by a common discontinuous controller with different control gains, which fills the gap in studying FFTBC issues with discontinuous protocols. Some numerical examples with comparisons are given to demonstrate the effectiveness of our designs.  相似文献   

15.
In this article, an adaptive fuzzy control method is proposed for induction motors (IMs) drive systems with unknown backlash-like hysteresis. First, the stochastic nonlinear functions existed in the IMs drive systems are resolved by invoking fuzzy logic systems. Then, a finite-time command filter technique is exploited to overcome the obstacle of “explosion of complexity” emerged in the classical backstepping procedure during the controller design process. Meanwhile, the effect of the filter errors generated by command filters is decreased by utilizing corresponding error compensating mechanism. To cope with the influence of backlash-like hysteresis input, an auxiliary system is constructed, in which the output signal is applied to compensate the effect of the hysteresis. The finite-time control technology is adopted to accelerate the response speed of the system and reduce the tracking error, and the stochastic disturbance and backlash-like hysteresis are considered to improve control accuracy. It’s shown that the tracking error can converge to a small neighborhood around the origin in finite-time under the constructed controller. Finally, the availability of the presented approach is validated through simulation results.  相似文献   

16.
In this paper, an adaptive neural control scheme is proposed for a class of unknown nonlinear systems with unknown sensor hysteresis. The radial basis function neural networks are employed to approximate the unknown nonlinearities and the backstepping technique is implemented to construct controllers. The difficulty of the control design lies in that the genuine states of the system are not available for feedback, which is caused by sensor hysteresis. The proposed control scheme eventually ensures the practical finite-time stability of the closed-loop system, which is proved by the Lyapunov theory. A numerical simulation example is included to verify the effectiveness of the developed approach.  相似文献   

17.
This paper is concerned with the problem of dynamic surface asymptotic tracking for a class of uncertain nonlinear systems preceded by Bouc–Wen type of hysteresis nonlinearity. By introducing the nonlinear filters with a positive time-varying integral function, a novel robust adaptive control algorithm is presented without constructing the hysteresis inverse. Unlike some existing adaptive control schemes for systems with input hysteresis, the proposed controller not only solves the issue of “explosion of complexity” inherent in the recursive procedure, but also produces the asymptotic tracking in spite of input hysteresis and external disturbances. Finally, two simulation examples are presented to confirm the effectiveness of the developed control strategy.  相似文献   

18.
This paper presents the optimal quadratic-Gaussian controller for uncertain stochastic polynomial systems with linear control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As intermediate results, the paper gives closed-form solutions of the optimal regulator and controller problems for stochastic polynomial systems with linear control input and a quadratic criterion. Performance of the obtained optimal controller is verified in the illustrative example against the conventional quadratic-Gaussian controller that is optimal for stochastic polynomial systems with known parameters. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included.  相似文献   

19.
An output feedback control analysis and design framework for linear systems with input hystereses nonlinearities is developed. Specifically, by transforming the hystereses nonlinearities into dissipative input-output dynamical operators, dissipativity theory is used to analyze and design linear controllers for systems with hysteretic actuators. The overall framework guarantees partial asymptotic stability of the closed-loop system; that is, asymptotic stability with respect to part of the closed-loop system state associated with the plant and the controller. Furthermore, the remainder of the state associated with the hysteresis dynamics is shown to be semistable; that is, solutions of the hysteretic system converge to Lyapunov stable equilibrium points determined by the system initial conditions.  相似文献   

20.
The problem of existence of almost periodic solutions of uncertain impulsive functional differential systems of fractional order is investigated. Using the Lyapunov method combined with the concept of uniformly positive definite matrix functions and Hamilton–Jacobi–Riccati inequalities new criteria are presented. The robust stability of the almost periodic solution is also discussed. We apply our results to an impulsive Lasota–Wazewska type model of fractional order. Our results extend the theory of almost periodic solutions for impulsive delay differential equations to the fractional-order case under uncertainty.  相似文献   

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