Showing papers presented at "Conference on Decision and Control in 1992"

Stable adaptive fuzzy control of nonlinear systems

Abstract: The author develops a direct adaptive fuzzy controller which does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy control rules directly into the controllers, and guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. The specific formula of the bounds is provided so that controller designers can determine the bounds based on their requirements. The direct adaptive fuzzy controller is used to regulate an unstable system to the origin. Simulation results show that the direct adaptive fuzzy controller can perform successful control without using any fuzzy control rules. After incorporating some fuzzy control rules into the controllers the adaptation speed became much faster. The author also showed explicitly how the supervisory control forced the state to be within the constraint set and how the adaptive fuzzy controller learned to regain control. >

Coordinating locomotion and manipulation of a mobile manipulator

Abstract: A planning and control algorithm for coordinating the motion of a mobile manipulator is presented. The design criterion is to control the mobile platform so that the manipulator is maintained in a configuration which maximizes the manipulability measure. The effectiveness of the method was verified by simulations on two representative trajectories. The algorithm was implemented with an actual mobile manipulator and tested on one of the trajectories for comparison purposes. >

Nonholonomic control systems: from steering to stabilization with sinusoids

Abstract: The authors present a control law for globally asymptotically stabilizing a class of controllable nonlinear systems without drift. The control law combines earlier work in steering nonholonomic systems using sinusoids at integrally related frequencies, with the ideas in recent results on globally stabilizing linear and nonlinear systems through the use of saturation functions. Simulation results for stabilizing a simple kinematic model of an automobile are included. >

Sliding-mode observers based on equivalent control method

Abstract: The sliding-mode observer for a nonlinear system is proposed. The observer is based on the equivalent control method. Compared with the known output global linearization approach it is given in terms of the system variables and does not require nonlinear state transformation. Several examples are presented which illustrate the proposed method. >

Neural networks in control systems

Abstract: Some of the problems that arise in the control of nonlinear systems in the presence of uncertainty are considered Multilayer neural networks and radial basis function networks are used in the design of identifiers and controllers, and gradient methods are used to adjust their parameters For a restricted class of nonlinear systems, it is shown that globally stable adaptive controllers can be determined Simulation results are presented to demonstrate that the methods presented can be used for the effective control of complex nonlinear systems >

An introduction to motion planning under multirate digital control

Abstract: The authors propose digital control methods for steering real analytic controllable systems between arbitrary state configurations. The main idea is to achieve a multirate sampled procedure to perform motions in all the directions of controllability under piecewise constant controls. When it is applied to non-holonomic control systems without drift, the procedure simplifies. In particular, it results in exact steering on chained systems recently introduced in the motion planning literature. A classical example is reported. >

The supervisory control of timed discrete-event systems

Abstract: The framework given by P.J. Ramadge and W.M. Wonham (SIAM J. Control Optim., Vol. 25, no.1, p.206-30, 1987) for control of discrete event systems is augmented with timing features by use of Ostroff's semantics for timed transition models (1989, 1990). It is shown that the corresponding concept of controllability, and the existence of minimally restrictive supervisory controls can be suitably generalized. The enhanced setting admits subsystem composition, and the concept of forcible event as an event that preempts the tick of a global clock. An example of a simple manufacturing cell illustrates how the new framework can be used to solve synthesis problems which may include logic-based, temporal and quantitative optimality specifications. >

Integrated probabilistic data association (IPDA)

Abstract: A version of the probabilistic data association (PDA) algorithm that is called integrated probabilistic data association (IPDA) is presented. Rather than deriving algorithms based on an assumption of track existence, IPDA starts from expressions which treat track existence as an event with an associated probability. This approach leads to a set of recursive formulae for both data association and probability of track existence or track quality. This is useful in the track initiation phase (to confirm a tentative track) and in track termination (to terminate a false track). The IPDA algorithm is compared with both the probabilistic data association algorithm (PDA) and the interactive multiple model (IMM) PDA algorithm. >

Optimal stochastic estimation with exponential cost criteria

Abstract: The expected value of the exponential of a weighted quadratic sum of the squares of the estimation error is minimized with respect to the state estimate subject to a Gauss-Markov system. The state estimates are assumed to be a function of the measurement history up to the stage time of the state vector. The estimator which optimizes this exponential cost criterion is linear but is not a conditional mean estimator such as the Kalman filter. This shows that the implications of Sherman's theorem are restricted to functions of the estimates which have access to the same measurement history such as in smoothing problems. In the solution process the expectation operation is replaced by an extremization operation allowing the formulation of a deterministic discrete time game. The saddle point estimator resulting from this game is the same as that obtained from the solution of an associated disturbance attenuation problem. This optimal stochastic estimator which generalizes the Kalman filter can feature the estimation error of certain states over others by the choice of the quadratic weighting matrices in the cost criterion. Correlation between the measurement and process noises is included. >

Semiglobal stabilization of a class of nonlinear systems using output feedback

Abstract: The stabilization of a class of multivariable nonlinear systems, about an equilibrium point at the origin, using output feedback is considered. Emphasis is placed on a class of systems that can be transformed into a global normal form with no zero dynamics. Semiglobal stabilization means that for every compact set of initial conditions, it is possible to design an output feedback controller that stabilizes the origin and includes the given compact set in the region of attraction. The system equations are allowed to depend on constant unknown parameters that do not change the vector relative degree of the system. The controller is robust with respect to these parameters. Global Lipschitz conditions are not required. >

Robust nonlinear controller design for transient stability enhancement of power systems

Abstract: A robust DFL (direct feedback linearization) nonlinear excitation controller is proposed to enhance transient stability for power systems. A robust control technique for linear systems is extended to design this controller. The design of the controller is independent of the operating point. Simulation results show that the controller has the following advantages: the fault location does not need to be known and the controller can overcome the variation of the reactance of the transmission line. Both transient stability enhancement and voltage regulation can be achieved. >

H/sub infinity /-optimal estimation: a tutorial

Abstract: The different aspects of H/sub infinity / estimation of linear, time-varying processes are considered, in both the continuous- and the discrete-time cases. The connection with differential games is explained and the uniqueness and robustness issues are discussed. Four illustrative examples are given that demonstrate the various estimation schemes and compare the H/sub infinity / results with the corresponding L/sub 2/ solutions. >

Backstepping to passivity: recursive design of adaptive systems

Abstract: A major obstacle to the wider use of the passivity concept has been its limitation to systems of relative degree one. The relative degree limitation has been effectively removed by various forms of a recursive procedure called backstepping. It is shown how backstepping is used to design a generation of adaptive controllers for nonlinear systems. The backstepping procedure provides a framework for recursive designs by achieving, at each step, the strict passivity of a virtual system. In addition to boundedness, the systems designed by this procedure also possess strong convergence properties. >

Pseudolinearization of the acrobot using spline functions

Abstract: The authors present an algorithm for the construction of approximation to both the nonlinear control and coordinate transformation under which a single-input nonlinear system has a linear tangent model independent of its operating point. Substituting spline approximations for functions that can be difficult to compute yields a stable closed-loop system with an arbitrarily small deterioration in performance. The approximate pseudolinearization control law is easy to calculate and inexpensive to implement, regardless of the complexity of the nonlinear model. Experimental results obtained by implementing the approximate pseudolinearization control law on a remotely driven acrobot verify the controller's ease of design and computational efficiency. >

Modeling and analysis of hybrid control systems

Abstract: A hybrid control system is a continuous-time system modeled by differential equations, and the controller is a discrete event system modeled by an automaton. A framework for modeling hybrid control systems, including the necessary interface between the plant and controller is presented. A method to represent the entire system as a discrete event system is shown. The concept of determinism is used to analyze hybrid control system behavior and guide in hybrid control system design. >

Two subspace algorithms for the identification of combined deterministic-stochastic systems

Abstract: Two new subspace algorithms for identifying mixed deterministic-stochastic systems are derived. Both algorithms determine state sequences through the projection of input and output data. These state sequences are shown to be outputs of nonsteady-state Kalman filter banks. From these it is easy to determine the state space system matrices. The algorithms are always convergent (noninterative) and numerically stable since they only make use of QR and singular value decompositions. The two algorithms are similar, but the second one trades off accuracy for simplicity. An example involving a glass oven is considered. >

Design of nonlinear generator exciters using differential geometric control theories

Abstract: The authors present the design of a nonlinear excitation system for synchronous generators which allows the generators to achieve improved damping performance in voltage dynamics. For illustrative purposes, the proposed control is demonstrated on a simple three-bus system. Designs that use differential geometric control theories, namely, exact and partial feedback linearizing techniques, are considered. The intent is to explore the potentiality of nonlinear exciters; these designs are much different from their linear counterpart. >

Neural networks as on-line approximators of nonlinear systems

Abstract: The authors present an approximation theory perspective in the design and analysis of nonlinear system identification schemes using neural network and other online approximation models. The identification procedure considered is based on a discrete-time formulation. Depending on the location of the adjustable parameters, networks are classified into linearly and nonlinearly parametrized networks. Based on this classification, a unified procedure for modeling discrete-time dynamical systems using online approximators is developed. The proposed identification methodology guarantees stability of the overall system even in the presence of modeling errors, and upper bounds for the average output error are obtained in terms of the modeling error. Simulation studies are used to illustrate the results and to compare different approximation models. >

A differential-algebraic condition for controllability and observability of time varying linear systems

Abstract: An algebraic rank condition for controllability and observability of time-varying linear systems is given. The time-varying structure matrix is expanded in generated Lie algebra, with respect to a basis. It is proved that under a differential-algebraic condition for the time-dependent coefficients, controllability and observability are equivalent to a multivariable Kalman's condition, independent of the time-dependent terms. >

Sensitivity of Hopf bifurcations to power system parameters

Abstract: Formulas for the sensitivity of the Hopf loading margin with respect to any power system parameter are presented. These first-order sensitivities determine an optimum direction in parameter space for changing parameters to increase the loading margin. The Hopf bifurcation sensitivities of a simple power system with a voltage regulator and a dynamic load model are computed. Parameter sensitivities of the Hopf and saddle node bifurcations are compared. An idea for eliminating some Hopf bifurcations is presented. >

Adaptive friction compensation for bi-directional low-velocity position tracking

Abstract: A comparative investigation of friction-compensating control strategies designed to improve low-velocity reversals for servomechanisms is presented. The methods considered include adaptive control and estimation-based control. The various controller designs incorporate different friction models ranging from classical friction and Stribeck friction to the less popular Dahl friction model. The control strategies are compared in an extensive test program involving sinusoidal position trajectory tracking experiments on a direct-drive DC motor. The results show that the adaptive and estimation-based controllers outperform more traditional linear controllers. It is also shown that the Dahl model, typically ignored in the literature, is significant for the friction-compensating control problem with repeated zero-velocity crossings. >

Robust stability and performance of uncertain systems in state space

Abstract: Robust performance analysis and state feedback design are considered for systems with time-varying parameter uncertainties. The notion of a strongly robust H/sub infinity / performance criterion is introduced, and its applications in robust performance analysis and synthesis for nominally linear systems with time-varying uncertainties are discussed and compared with the constant scaled small gain criterion. It is shown that most robust performance analysis and synthesis problems under this strongly robust H/sub infinity / performance criterion can be transformed into linear matrix inequality problems, and can be solved through finite-dimensional convex programming. The results are in general less conservative than those obtained using small-gain-type criteria. >

An algorithm for state-space frequency domain identification without windowing distortions

Abstract: An algorithm is presented for identifying state space models from frequency domain data. The main advantage of this approach is that it avoids windowing distortions associated with other frequency domain methods. Other advantages are that an arbitrary frequency weighting can be introduced to shape the estimation error, and the system order can be overspecified. The numerical properties are demonstrated on real physical data taken on a complex flexible structure, resulting in an identified state-space model with 74 states over a bandwidth of 128 Hz. The results indicate that the algorithm would be useful in applications requiring the accurate identification of high-order systems over wide bandwidths. >

Robust control of a compact disc player

Abstract: The design of robust controllers for a compact disc mechanism is considered. Using mu synthesis, a controller has been designed for good track-following. The design problem involves time-domain constraints on signals and robustness requirements for norm-bounded structured plant uncertainty. It is shown that by using weighting functions in the mu framework this problem can be solved, but at the cost of many design iterations. The mu controller has been implemented in an experimental setup with a digitally controlled compact disc player. >

Iterative learning control-convergence using high gain feedback

Abstract: The author presents a convergence theory for iterative learning control based on the use of high-gain current trial feedback for the special case of relative degree one, MIMO (multiple-input multiple-output) minimum-phase systems. The results are related to those of Padieu and Su (1990) via the notion of positive real systems. In particular, positive real systems are easily arranged to have convergent learning by simple proportional learning rules of arbitrary positive gain. >

Modelling methods for improving robustness in fault diagnosis of jet engine system

Abstract: Modeling uncertainty is an inevitable consequence of the complexity of jet engine systems, and accurate dynamic models can never be fully obtained. The authors concentrate on the derivation of suitable mathematical models of a jet engine, to enable robust fault diagnosis designs to be achieved. The modeling uncertainty can be described as an additional term in the dynamic structure. Based on this structure, a robust fault diagnosis scheme can be designed. New methods are presented for determining the structure of modeling uncertainty. The work uses a 17th order nonlinear jet engine simulation model to illustrate the methods proposed. The simulation results show the power of the method in modeling jet engine systems for robust fault diagnosis purposes. >

Monitoring cooperative equilibria in a stochastic differential game

Abstract: The authors study a class of equilibria for stochastic differential games which are based on monitoring an implicit cooperative solution. The equilibrium is reached by implementing a random triggering scheme which changes the mode of play when there is an indication that at least one player may be departing from the cooperative solution. These equilibria make use of a particular kind of memory strategy and exploit the nonuniqueness of the solution to an associated Hamilton-Jacobi-Bellman (HJB) equation. In particular, it is shown that these equilibria, which satisfy a continuous-time dynamic programming equation, can be designed in such a way that they generate payoffs which dominate those obtained via the classical feedback Nash equilibrium for the original stochastic diffusion game. >

Minimum-time control for uncertain discrete-time linear systems

Abstract: Linear discrete-time uncertain systems with control and state constraints are discussed. The problem of reaching and ultimately bounding the state in an assigned target set in minimum time is considered. A solution based on the construction of the domain of attraction to the target set in terms of controllability sets is given. A linear programming algorithm for the construction of such a domain is proposed for the case in which linear constraints are considered. >

Piezoelectric actuator design for vibration suppression: placement and sizing

Abstract: The authors consider the problem of simultaneous placement and sizing of distributed piezoelectric actuators to achieve the control objective of damping vibrations in a uniform beam. For several closed-loop performance measures they obtain optimal placement and sizing of the actuators using a simple numerical search algorithm. These measures are applied to a specific example of a simply supported beam with piezoelectric actuators, and their relative effectiveness is discussed. >

B/sup 3/ algorithm for robust performances analysis in presence of mixed parametric and dynamic perturbations

Abstract: The performance robustness of control systems in the presence of both parametric perturbations and unmodeled dynamics is investigated. Assuming polynomial parametric perturbations and H/sub infinity / performances, the problem is reduced to checking the positivity of suitable polynomials. A novel algorithm based on the Bernstein polynomial expansion is proposed. A Bernstein branch and bound (B/sup 3/) algorithm has been implemented using the formulas of Bernstein coefficients on subdivisions in the parameter space. The efficiency of the algorithm is demonstrated on some examples taken from the literature on the robustness analysis of nonlinearity perturbed control systems. >