Showing papers presented at "Conference on Decision and Control in 1998"

Output tracking control design of a helicopter model based on approximate linearization

Abstract: Output tracking control of a helicopter model is investigated. The model is derived from Newton-Euler equations by assuming that the helicopter body is rigid. First, we show that for several choices of output variables exact input-output linearization fails to linearize the whole state space and results in having unstable zero dynamics. By neglecting the couplings between moments and forces, we show that the approximated system with dynamic decoupling is full state linearizable by choosing positions and heading as outputs. We prove that bounded tracking is achieved by applying the approximate control. Next, we derive a diffeomorphism showing that an approximation of the system is differentially flat, thus state trajectory and nominal inputs can be generated from a given output trajectory. Simulation results using both output tracking controllers based on exact and approximate input-output linearization are presented for comparison.

Analysis of linear systems with saturation using convex optimization

Abstract: We show how linear matrix inequalities (LMI) can be used to perform local stability and performance analysis of linear systems with saturating elements. This leads to less conservative information on stability regions, disturbance rejection, and L/sub 2/-gain than standard global stability and performance analysis. The circle and Popov criteria are used to obtain Lyapunov functions whose sublevel sets provide regions of guaranteed stability and performance within a restricted state space region. Our LMI formulation leads directly to simple convex optimization problems that can be solved efficiently as semidefinite programs. The results cover both single and multiple saturation elements and can be immediately extended to discrete time systems. An obvious application of these techniques is in the analysis of control systems with saturating control inputs.

Critical power for asymptotic connectivity

Abstract: In wireless data networks the range of each transmitter, and thus its power level, needs to be high enough to reach the intended receivers, while being low enough to avoid generating interference for other receivers on the same channel. If the nodes in the network are assumed to cooperate, perhaps in a distributed and decentralized fashion, in routing each others' packets, as is the case in ad hoc wireless networks, then each node should transmit with just enough power to guarantee connectivity of the overall network. Towards this end, we determine the critical power at which a node in the network needs to transmit in order to ensure that the network is connected with probability one as the number of nodes in the network goes to infinity. Our main result is this: if n nodes are located randomly, uniformly i.i.d., in a disc of unit area in /spl Rfr//sup 2/ and each node transmits at a power level so as to cover an area of /spl pi/r/sup 2/=(log n + c(n))/n, then the resulting network is asymptotically connected with probability one if and only if c(n)/spl rarr/+/spl infin/.

Incorporation of time delayed measurements in a discrete-time Kalman filter

Abstract: In many practical systems there is a delay in some of the sensor devices, for instance vision measurements that may have a long processing time. How to fuse these measurements in a Kalman filter is not a trivial problem if the computational delay is critical. Depending on how much time there is at hand, the designer has to make trade offs between optimality and computational burden of the filter. In this paper various methods in the literature along with a new method proposed by the authors will be presented and compared. The new method is based on "extrapolating" the measurement to present time using past and present estimates of the Kalman filter and calculating an optimal gain for this extrapolated measurement.

A comprehensive study of control design for an autonomous helicopter

Abstract: We compare three different control methodologies for helicopter autopilot design: linear robust multivariable control, fuzzy logic control with evolutionary tuning, and nonlinear tracking control. The control design is based on nonlinear dynamic equations with a simplified thrust-torque generation model valid for hovering and low velocity flight. We verify the controller performance in various simulated manoeuvres.

Predictive control of teleoperated constrained systems with unbounded communication delays

Abstract: We present a control technique which allows the teleoperation of systems subject to input/state constraints through transmission channels with unbounded time-delays, such as Internet TCP/IP connections. The main idea is based on the fact that predictive controllers provide, as a by-product, command sequences which can be executed as emergency maneuvers whenever the communication channel is broken by excessive time-delays. We show how this idea can be exploited by equipping the predictive controller with some additional control logic which enables the synchronization between plant, predictive controller, and human operator.

Coordinated decentralized protocols for failure diagnosis of discrete event systems

Abstract: Addresses the problem of failure diagnosis in discrete event systems with decentralized information. We propose a coordinated decentralized architecture consisting of two local sites communicating with a coordinator that is responsible for diagnosing the failures occurring in the system. We extend the notion of diagnosability, originally introduced in Sampath et al. (1995) for centralized systems, to the proposed coordinated decentralized architecture. We specify three protocols that realize the proposed architecture. We analyze the diagnostic properties of these protocols. The key features of the proposed protocols are: (i) they achieve, each under a set of assumptions, the same diagnostic performance as the centralized diagnoser; and (ii) they highlight the performance vs. complexity tradeoff that arises in coordinated decentralized architectures.

PLC-based implementation of supervisory control for discrete event systems

Abstract: The supervisory control theory is a general theory for automatic synthesis of controllers (supervisors) for discrete event systems, given a plant model and a specification for the controlled behavior. Though the theory has for over a decade received substantial attention in academics, still very few industrial applications exist. The main reason for this seems to be a discrepancy between the abstract supervisor and its physical implementation. This is specifically noticeable when the implementation is supposed to be based on programmable logic controllers (PLCs), as is the case with many manufacturing systems. The asynchronous event-driven nature of the supervisor is not straightforwardly implemented in the synchronous signal-based PLC. We point out the main problems of supervisor implementation on a PLC, and suggest procedures to alleviate the problems.

Reducing conservativeness in predictive control of constrained systems with disturbances

Abstract: Predictive controllers which are able to guarantee constraint fulfilment in the presence of input disturbances, typically based on min-max formulations, often suffer excessive conservativeness. One of the main reasons for this is that the control action is based on the open-loop prediction of the evolution of the system, because the uncertainty due to the disturbance grows as time proceeds on the prediction horizon. On the other hand, such an effect can be moderated by adopting a closed-loop prediction. In this paper, closed-loop prediction is achieved by including a free feedback matrix gain in the set of optimization variables. This allows one to balance computational burden and reduction of conservativeness.

Adaptive stochastic approximation by the simultaneous perturbation method

Abstract: Stochastic approximation (SA) has long been applied for problems of minimizing loss functions or root-finding with noisy input information. As with all stochastic search algorithms, there are adjustable algorithm coefficients that must be specified and that can have a profound effect on algorithm performance. It is known that picking these coefficients according to an SA analogue of the deterministic Newton-Raphson algorithm provides an optimal or near-optimal form of the algorithm. This paper presents a general adaptive SA algorithm that is based on an easy method for estimating the Hessian matrix at each iteration while concurrently estimating the primary parameters of interest. The approach applies in both the gradient-free optimization (Kiefer-Wolfowitz) and root-finding/stochastic gradient-based (Robbins-Monro) settings and is based on the "simultaneous perturbation" idea introduced previously.

Computing polyhedral approximations to flow pipes for dynamic systems

Abstract: This paper presents a new approach to approximating the flows of continuous time dynamic systems from sets of initial conditions. The reachable set, or flow pipe, over a time interval [0, t/sub f/] is approximated by the union of a sequence of convex polyhedra. Each polyhedron contains a segment of the flow pipe. Properties of the approximation technique are discussed and illustrated with examples for linear and nonlinear systems, including the application of flow pipe approximation to verification of a simple hybrid system.

A note on input-to-state stability of sampled-data nonlinear systems

Abstract: It is shown for nonlinear systems that sampling sufficiently fast an input-to-state stabilizing (ISS) continuous time control law results in an ISS sampled-data control law. Two main features of our approach are: we show how the nonlinear sampled-data system can be modeled by a functional differential equation (FDE); and we exploit a Razumikhin type theorem for ISS of FDE that was proved by Teel (1998) to analyze the sampled-data system.

Simulation-based optimization of Markov reward processes

Abstract: We propose a simulation-based algorithm for optimizing the average reward in a Markov reward process that depends on a set of parameters. As a special case, the method applies to Markov decision processes where optimization takes place within a parametrized set of policies. The algorithm involves the simulation of a single sample path, and can be implemented online. A convergence result (with probability 1) is provided.

Control of LQG systems under communication constraints

Abstract: We examine the achievable control performance of an LQG system with a noisy analog feedback channel. To that end, we define the sequential rate distortion function. Assuming equi-memory, we show that the separation principle holds and that linear controllers are optimal. We give bounds on the optimal performance and show the inherent trade-offs between control and communication costs.

Fuzzy observers for nonlinear dynamic systems fault diagnosis

Abstract: This paper presents a new fault diagnosis scheme for nonlinear dynamic systems. In this scheme, the residual signal is generated by a fuzzy observer which is based on Takagi-Sugeno fuzzy models. The stability as well as eigenvalue constraint conditions for the fuzzy observer design are presented and solved in the linear matrix inequality framework. Finally, the paper demonstrates the application of fuzzy observers in detecting and isolating intermittent faults in the induction motor of a railway traction system.

Failure detection and identification and fault tolerant control using the IMM-KF with applications to the Eagle-Eye UAV

Abstract: We describe a novel approach to sensor/actuator failure detection and identification and fault tolerant control based on the interacting multiple model (IMM) Kalman filter approach. Failures are mapped into different (and unique) state-space model representations. The IMM algorithm computes (online) the posterior probability of each failure model, that can be interpreted as a failure indicator. The fault tolerant control approach presented is based on a multiple model control law, where an optimal controller is designed for each actuator failure model, and the control action is a combination of the individual outputs of each controller weighted by the posterior probability associated with that model. The new FDI-FTC approach was tested on a linear simulation of Bell Helicopter's Eagle-Eye unmanned air vehicle. All single sensor and actuator failures were detected and properly identified, as well as some simultaneous failures.

On the stability and existence of common Lyapunov functions for stable linear switching systems

Abstract: A sufficient condition for the existence of a common quadratic Lyapunov function (CQLF) for the linear systems x/spl dot/=A/sub i/x, A/sub i//spl isin/{A/sub 1/,A/sub 2/,...,A/sub m/}, A/sub i//spl isin/IR/sup n/spl times/n/ is that the matrices can be simultaneously triangularized using a non-singular transformation T. In this paper, we show that this result follows trivially from the structure of the matrices in the set A, and that the switching system, constructed by switching between the matrices in this set, is benign from a stability viewpoint. Finally, we then discuss several conditions under which a transformation T exists.

Tracking control of an underactuated surface vessel

Abstract: We consider tracking control of a surface vessel with only two control inputs. The surface vessel model has certain similarities with chained form systems, but cannot be transformed to chained form. In particular, the model has a drift vector field as opposed to the drift-free chained form systems. It is shown, however, that methods developed for tracking control of chained form systems, can be used for developing a tracking control law for the surface vessel. Through a coordinate transformation the model is put in a triangular-like form which makes it possible to use integrator backstepping to develop a tracking control law. The control law steers both the position variables and the course angle of the surface vessel, providing semi-global exponential stabilization of the desired trajectory.

Intelligent control of piezoelectric actuators

Abstract: An intelligent tracking control architecture is proposed for a class of continuous-time nonlinear dynamic systems actuated by piezoelectric actuators. Generally, hysteresis nonlinearity exists in the piezoelectric actuator, which may cause undesirable inaccuracy. Based on solutions of a general hysteresis model, an approximation function is introduced to compensate for effects of the hysteresis nonlinearities. This approximation function is implemented by fuzzy logic method, which is expressed as a series expansion of basis functions. Combining this approximation function with adaptive control techniques, an intelligent control algorithm is developed. As a result, global asymptotic stability of the system is established in the Lyapunov sense. Simulation results are included to demonstrate the control performance.

Hybrid systems and optimal control

Abstract: The aim of this paper is to treat some optimal control problems for a class of hybrid systems. We start providing a definition of hybrid system inspired by the concept introduced by Artstein (1995), who defines hybrid control in relation to stabilization problems for a classical control system. The same definition proved to be successful to tackle other stabilization problems. In this paper, we consider a class of systems with hybrid features and optimization problems for this class of systems. The word hybrid is motivated by the fact that these systems are characterized by the presence of both a continuous time evolution and a discrete time evolution. A trajectory for these systems evolves following some dynamical constraint and at some fixed or variable times (called location switching times) it jumps following the rules of a discrete time evolution. The definition of hybrid system we give is quite general and covers many interesting applications.

On global stabilization of Burgers' equation by boundary control

Abstract: Burgers' equation is a natural first step towards developing methods for control of flows. We derive nonlinear boundary control laws that achieve global asymptotic stability (in a very strong sense). We consider both the viscous and the nonviscous Burgers' equation, using both Neumann and Dirichlet boundary control. We also study the case where the viscosity parameter is uncertain, as well as the case of stochastic Burgers' equation. For some of the control laws that would require the measurement in the interior of the domain, we develop the observer-based versions.

A multiple model-based reconfigurable flight control system design

Abstract: We consider a problem of designing a reconfigurable control strategy that achieves acceptable flight performance in the presence of wing battle damage for a tailless advanced fighter aircraft (TAFA). This is a complex practical problem since wing damage results in abrupt variation in the aircraft dynamics. Hence fast and accurate control reconfiguration is vital for assuring aircraft survivability. Our suggested reconfigurable controller is based on the concept of multiple models, switching, and tuning. The overall control system consists of multiple parallel identification models, describing different percentages of wing damage, and corresponding controllers. Based on a suitably chosen switching mechanism, the system quickly finds the model that is closest to the current damage mode, and switches to the corresponding controller achieving excellent overall performance. In addition, the boundedness of the signals in the system is guaranteed if the switching interval is chosen to be sufficiently small. It is shown that the key element is the design of sufficiently robust individual controllers for each of the damage conditions. This has been accomplished using a combination of inverse dynamics and output error feedback control laws. The properties of the overall system are illustrated through simulations using linearized TAFA models provided by Boeing. Simulation results have demonstrated the potential of the multiple model-based approach to solve complex practical reconfigurable control design problems.

Rollout algorithms for stochastic scheduling problems

Abstract: Stochastic scheduling problems are difficult stochastic control problems with combinatorial decision spaces. We focus on a class of stochastic scheduling problems, the quiz problem and its variations. We discuss the use of heuristics for their solution, and we propose rollout algorithms based on these heuristics which approximate the stochastic dynamic programming algorithm. We show how the rollout algorithms can be implemented efficiently, with considerable savings in computation over optimal algorithms. We delineate circumstances under which the rollout algorithms are guaranteed to perform better than the heuristics on which they are based. We also show computational results which suggest that the performance of the rollout policies is near-optimal, and is substantially better than the performance of their underlying heuristics.

Hierarchical control of small autonomous helicopters

Abstract: Autonomous air vehicles have numerous applications, all of which require the vehicle to have stable and accurate control of its motion. In the paper, a hierarchical control system for small autonomous helicopters is described. The control system consists of four components: a navigation filter, an inner-loop hover control system, a waypoint guidance system, and a ground-based flight manager. All four elements of the control system have been verified with flight tests of the Draper small autonomous air vehicle.

Robust properties of risk-sensitive control

Abstract: It is well-known that there are strong connections between risk-sensitive stochastic control and deterministic H/sub /spl infin// control. These connections have stimulated interest in the risk-sensitive control problem. But is the risk-sensitive controller robust? This paper answers this question in an affirmative and precise way, and gives a stochastic small gain theorem and a stochastic robust stability result.

A multiple model predictive scheme for fault-tolerant flight control design

Abstract: The model predictive control (MPC) strategy is used as a basic control law within the framework of multiple models, switching and tuning to design a reconfigurable flight control system. The controller described can explicitly take into account hard constraints on control inputs, and achieve acceptable flight performance in the presence of control effector freezing. To arrive at an effective reconfigurable control design, a new parametrization of the aircraft model in the presence of control effector freezing is suggested. It turned out that such a parametrization is well suited for use within the MPC framework. The overall multiple model predictive control scheme quickly identifies the nature and time instant of the failure, and carries out automatic reconfiguration of the control law achieving acceptable flight performance. The properties of our reconfigurable controller are evaluated through simulations of an F/A-18A aircraft carrier landing manoeuvre in the presence of critical control effector failures.

Control of redundant manipulators using logic-based switching

Abstract: We study the control of redundant planar robotic manipulators using a switched (or hybrid) control scheme, focusing on manipulators with a degree of redundancy of one. We emphasize the effectiveness of switched control systems with respect to stabilization and performance enhancement for this class of manipulators. We present a simulation study of logic-based switching control of a 3-DOF planar manipulator under end-effector trajectory tracking and demonstrate the capabilities of this scheme.

Guaranteed recursive nonlinear state estimation using interval analysis

Abstract: The problem considered is state estimation in the presence of unknown state and measurement noise, each noise component being assumed to belong to some known interval. In such a bounded-error context, most available results are for linear models, and the purpose of the present paper is to deal with the nonlinear case. Based on interval analysis and the notion of set inversion, a new state estimator is presented, which evaluates a set estimate guaranteed to contain all values of the state that are consistent with the available observations, given the noise bounds and a set containing the initial value of the state. To the best of our knowledge, it is the first time that such a guaranteed estimator is made available. The precision of the set estimate can be improved, at the cost of more computation. The theoretical properties of the estimator are studied, and computer implementation has received special attention. A simple illustrative example is treated.

On the design of robust servomechanisms for minimum phase nonlinear systems

Abstract: We consider a single-input single-output nonlinear system which has a well defined normal form with asymptotically stable zero dynamics. We study the design of a robust output feedback controller, that incorporates a linear servo compensator, to achieve asymptotic tracking and disturbance rejection. We determine the least amount of precise information about the plant that is needed to design the controller. Such design will be robust to plant parameters and uncertainties which are not used in the design calculations. We also study the robustness of the design to errors in determining the linear servo compensator. Such errors could arise from approximating a general continuous nonlinear function by a polynomial one, or from errors in determining the frequencies of the exogenous signals. We give regional as well as semiglobal results.

Hinging hyperplane trees for approximation and identification

Abstract: The hinging hyperplane tree (HHT) model for the approximation of nonlinear mappings is proposed. The corresponding construction algorithm builds a binary tree-structured model based on nonlinear hinge functions. Unlike other tree-structured algorithms, this local model approach performs a recursive axis-oblique decomposition of the input space due to the location of the hinge functions. An extension of the hinging hyperplane trees with external dynamics is applied to the identification of a combustion engine turbocharger. Experimental results for the multiple-input single-output process are presented.