Linear Dynamic Control Research Articles

Singularity robust, dynamic linearization control algorithm for MK mobile robot

MK robot is a two wheel nonholonomic cart with driving moments referenced to a pendulum (the robot body). A modification of the described in (Tchoń et al., 2002) dynamic linearization control algorithm for MK robot is proposed, which provides singularity robust version of this algorithm. The simulation results show good performance of the modified algorithm even for trajectories which do not fit dynamic linearization algorithm restrictions.

H∞ controller synthesis for pendulum-like systems

This paper focus on a stabilization problem for a class of nonlinear systems with periodic nonlinearities, called pendulum-like systems. A notion of Lagrange stabilizability is introduced, which extends the concept of Lagrange stability to the case of controller synthesis. Based on this concept, we address the problem of designing a linear dynamic output controller which stabilizes (in the Lagrange sense) a pendulum-like system within the framework of the H ∞ control theory. Lagrange stabilizability conditions for uncertainty-free systems and systems with norm-bounded uncertainty in the linear part are derived, respectively. When these conditions are satisfied, the desired stabilization output feedback controller can be constructed via feasible solutions of a certain set of linear matrix inequalities (LMIs).

A Linear Quadratic Control for Discrete Systems with Random Parameters and Multiplicative Noise and Its Application to Investment Portfolio Optimization

A quadratic control for discrete stochastic systems with random parameters and additive and multiplicative noises dependent on state and controls is studied. Equations for the optimal linear static and dynamic output controllers are derived. The controllers are robust to the type of the distribution of the vector of random parameters. The results are applied to dynamic investment portfolio optimization.

Robust H ∞ control of a class of nonlinear uncertain time-delay systems

The robust H∞ control problem of a class of uncertain nonlinear time-delay systems is considered in this paper. The parametric uncertainties are real time-varying and norm-bounded and the nonlinearities are state-dependent and cone-bounded. The delays are time-varying and bounded both in the state and at the input. We provide sufficient conditions for robust stability and robust state-feedback stabilization with disturbance attenuation. Then, we establish sufficient conditions for designing a linear dynamic observer-based controller which stabilizes the uncertain time-delay system and guarantees an H∞-norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays. Several examples are simulated to illustrate the developed theory.

Robust $ {\cal H}_{\infty}$ Control of a Class of Nonlinear Uncertain Time-Delay Systems

The robust $ {\cal H}_{\infty}$ control problem of a class of uncertain nonlinear time-delay systems is considered in this paper. The parametric uncertainties are real time-varying and normbounded and the nonlinearities are state-dependent and cone-bounded. The delays are time-varying and bounded both in the state and at the input. We provide sufficient conditions for robust stability and robust state-feedback stabilization with disturbance attenuation. Then, we establish sufficient conditions for designing a linear dynamic observer-based controller which stabilizes the uncertain time-delay system and guarantees an $ {\cal H}_{\infty}$ -norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays. Several examples are simulated to illustrate the developed theory.

An Identification Algorithm for a Linear Discrete Dynamic Control System

A problem of developing an identification algorithm for a linear discrete dynamic control system is considered. The solution is based on the derived formulas for the differentiation of quadratic functionals with respect to matrix variables. An example is given.

線形ダイナミカルシステムの対称性と制御 (モデリングと制御器設計の接点-システム表現を考える特集号)

線形ダイナミカルシステムの対称性と制御 (モデリングと制御器設計の接点-システム表現を考える特集号)

Positive real analysis and synthesis of uncertain discrete time systems

The positive real analysis and synthesis problems for a class of uncertain discrete-time systems are considered. The uncertainties are expressed in a linear fractional form. The analysis problem is to characterize conditions for a which the uncertain discrete-time system is positive real for all admissible uncertainties. A linear matrix inequality (LMI)-based analysis result is derived. The synthesis problem is to design linear state-feedback and dynamic output-feedback controllers that robustly stabilize the uncertain discrete-time system and achieve the strict positive realness for the closed-loop transfer functions. It has been established that the problems above can be cast into a class of parameterized strict positive real control problems without uncertainties.

パラメータ表現された出力フィードバックスライディングモード制御器に関する研究

In this paper, a parameterizaton of output feedback dynamic sliding mode controller is proposed and the BIBO stability problem of generalized plant is studied. It is shown that by the proposed controller, the sliding mode is achieved in finite time, and thereafter, the ideal sliding mode controller stabilizes the generalized plant in the sense that the slightly modified BIBO stability is assured. Also, the model matching problem is formulated for this controller and the difference between linear dynamic controller and sliding mode controller is highlighted.

Robust nonlinear H/sub ∞/ synchronization of chaotic Lur'e systems

We propose a method of robust nonlinear H/sub /spl infin// master-slave synchronization for chaotic Lur'e systems with applications to secure communication. The scheme makes use of vector field modulation and either full static state or linear dynamic output error feedback control. The master-slave systems are assumed to be nonidentical and channel noise is taken into account. Binary valued continuous time message signals are recovered by minimizing the L/sub 2/-gain from the exogenous input to the tracking error for the standard plant representation of the scheme. The exogenous input takes into account the message signal, channel noise and parameter mismatch. Matrix inequality conditions for dissipativity with finite L/sub 2/-gain of the standard plant form are derived based on a quadratic storage function. The controllers are designed by solving a nonlinear optimization problem which takes into account both channel noise and parameter mismatch. The method is illustrated on Chua's circuit.

Dissipative controllers for nonlinear multibody flexible space systems

The problem of controlling a class of nonlinear multibody flexible space systems is considered. The system configuration consists of a flexible central body to which a number of flexible articulated appendages are attached, resulting in highly nonlinear dynamics. Assuming collocated actuators and sensors, global asymptotic stability of such systems is established using a nonlinear passivity-based control law. In addition, a special case where the central-body motion is small while the appendages can undergo unlimited motion, it is shown that the system, although highly nonlinear, can be stabilized by linear static and dynamic dissipative control laws. Furthermore, the static dissipative control law preserves stability despite actuator and sensor nonlinearities of certain types. In all cases, the stability does not depend on the knowledge of the model and hence is robust to modeling errors and uncertainties. The results are applicable to a broad class of systems, such as flexible multilink manipulators and multipayload space platforms. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems.

Persistent disturbance rejection via static-state feedback

In contrast with /spl Hscr//sub /spl infin// and /spl Hscr//sub 2/ control theories, the problem of persistent disturbance rejection (l/sup 1/ optimal control) leads to dynamic controllers, even when the states of the plant are available for feedback. Using viability theory, Shamma showed (1993), in a nonconstructive way, that in the state-feedback case the same performance achieved by any dynamic linear time-invariant controller can be achieved using memoryless nonlinear state feedback. In this paper we give an alternative, constructive proof of these results for discrete- and continuous-time systems. The main result of the paper shows that in both cases, the l/sup 1/ norm achieved by any stabilizing state-feedback linear dynamic controller can be also achieved using a memoryless variable structure controller. >

Gain scheduling dynamic linear controllers for a nonlinear plant

For a general type of nonlinear tracking problem, we consider gain scheduling based on a family of linear dynamic controllers designed for a family of plant linearizations about constant operating points. A necessary and sufficient condition for the existence of gain scheduled controllers satisfying appropriate requirements is presented. Using this condition, the impact of linear controller configuration on the existence of a gain scheduled controller can be assessed, and ad hoc approaches to scheduling can be analyzed.

On some structures of stabilizing control laws for linear and time-invariant systems with bounded point delays and unmeasurable states

The output-feedback stabilization is considered by linear dynamic controllers of (open-loop) stabilizable and detectable time-invariant plants involving a finite set of bounded internal point delays. Two controllers involving, respectively, point and distributed delays are studied as well as their extension to the use of a feedback signal consisting of convolutions of the system output and controller state with an appropriately chosen linearly independent set of functions. It is concluded that an increase in the order of the controller dynamics can be used as an alternative stabilization technique to the use of delays in the controller.

Gain scheduling for H-infinity controllers: a flight control example

A new approach to gain scheduling linear dynamic controllers is illustrated for a pitch-axis autopilot design problem. In this application the linear controllers are designed at distinct operating conditions by H/sup infinity / methods. The gain scheduling procedure uses particular features of both the linear dynamic controllers and the controller configuration to remove so-called hidden coupling terms that can occur in scheduled controllers. Potential performance improvement is demonstrated by comparing simulation results to those for a naive gain scheduled controller that ignores the coupling terms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Vibrational feedback control in the problem of acoustic stability

The problem of absolute stability in a vibrational feedback controller is introduced and discussed. It is shown that for any rational G(s)=n(s)/d(s) with d(s) Hurwitz and deg d(s) -deg n(s)=1 there exists a linear dynamic periodic controller that ensures, in a certain sense, the infinite sector of absolute stability. This implies that an additional dynamical element, inserted in the feedback loop, may lead to improvements in the robustness of nonlinear systems. >

Geometric approach for fault diagnosis in linear dynamic control systems

A method for multiple fault diagnosis of plants described by a linear difference model is proposed in the form of an algorithm. The algorithm is based on the observation that, when the number of faulty units of the system is known, the set of faulty units can be differentiated from other sets by checking linear varieties in the measurement data space. It is further shown that the system with t number of faults can be diagnosed within (t+1) sample/time units if the input-output measurements are rich and that the algorithm can be used for diagnosis even when the number of faults is not known in advance.

Quantization and overflow effects in digital implementations of linear dynamic controllers

The stability of a class of single-input/single-output (SISO) digital-feedback control systems is investigated. The systems considered contain a linear dynamic plant, a digital controller, and suitable D/A (digital-to-analog) and A/D converters. The design of such systems is usually accomplished by ignoring the nonlinear effects caused by quantization and overflow truncation. Simulations of specific examples establish the quantization in such systems can lead to loss of asymptotic stability of the origin. Obtained results prove that when quantization is taken into account (but overflow is neglected), one only has convergence to some (small) neighborhood about the origin. The results also prove that for initial conditions sufficiently far from the origin, overflow effects can lead to unbounded solutions. In particular, this is the case for observable systems with at least one eigenvalue in the open right-half plane (RHP). The case of systems with no eigenvalues in the open RHP, but with eigenvalues on the j omega -axis, is still unresolved. >

Stabilizability of linear time-varying and uncertain linear systems

Feedback stabilization of linear time-varying and uncertain linear systems is considered. It is proved that given a stabilizing dynamic linear state-feedback controller, one can always construct a stabilizing nondynamic linear state-feedback controller. A similar result is shown for uncertain linear systems. A linear time-varying system can be stabilized by dynamic output feedback if and only if it admits a coprime factorization. >

Decoupling and pole-zero assignment of singular systems with dynamic state feedback

This paper refers to the problem of designing a linear state feedback dynamic controller for single-input, single-output decoupling of linear, time-invariant, singular systems. Sufficient conditions are established for the state-feedback decoupling problem to have a solution. In the case where the system satisfies these conditions, the class of controller matrices which decouple the system is given. Finally a method is presented for pole-zero placement in the decoupled singular system and a structure is described for the realization of the generalized transfer function matrices.