Peter Seiler

An H/sub /spl infin// approach to networked control

In this paper, we study the effect of a network in the feedback loop of a control system. We use a stochastic packet-loss model for the network and note that results for discrete-time linear systems with Markovian jumping parameters can be applied. We measure performance using an H/sub /spl infin// norm and compute this norm via a necessary and sufficient matrix inequality condition. We also derive necessary and sufficient linear matrix inequality (LMI) conditions for the synthesis of the H/sub /spl infin// optimal controller for a discrete-time jump system. Finally, we apply these results to study the effect of communication losses on vehicle control.

Disturbance propagation in vehicle strings

This note focuses on disturbance propagation in vehicle strings. It is known that using only relative spacing information to follow a constant distance behind the preceding vehicle leads to string instability. Specifically, small disturbances acting on one vehicle can propagate and have a large effect on another vehicle. We show that this limitation is due to a complementary sensitivity integral constraint. We also examine how the disturbance to error gain for an entire platoon scales with the number of vehicles. This analysis is done for the predecessor following strategy as well as a control structure where each vehicle looks at both neighbors.

Estimation with lossy measurements: jump estimators for jump systems

In this paper, we consider estimation with lossy measurements. This problem can arise when measurements are communicated over wireless channels. We model the plant/measurement loss process as a Markovian jump linear system. While the time-varying Kalman estimator (TVKE) is known to be optimal, we introduce a simpler design, termed a jump linear estimator (JLE), to cope with losses. A JLE has predictor/corrector form, but at each time selects a corrector gain from a finite set of precalculated gains. The motivation for the JLE is twofold. The computational burden of the JLE is less than that of the TVKE and the estimation errors expected when using JLE provide an upper bound for those expected when using TVKE. We then introduce a special class of JLE, termed finite loss history estimators (FLHE), which uses a canonical gain selection logic. A notion of optimality for the FLHE is defined and an optimal synthesis method is given. The proposed design method is compared to TVKE in a simulation study.

Brief paper: Local stability analysis using simulations and sum-of-squares programming

The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite-dimensional polynomial parametrizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates is assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on small examples from the literature and several control oriented systems.

A bounded real lemma for jump systems

This note presents a bounded real lemma for discrete-time Markovian jump linear systems (MJLSs). We show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems. For the case of one plant mode, this condition reduces to the standard necessary and sufficient condition for discrete-time systems. We envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for MJLSs.

Development of a Collision Avoidance System

The analysis of a rear-end collision warning/ avoidance (CW/CA) system algorithm will be presented. The system is designed to meet several criteria: 1. System warnings should result in a minimum load on driver attention. 2. Automatic control of the brakes should not interfere with normal driving operation.

Wind Turbine Fault Detection Using Counter-Based Residual Thresholding

Abstract Up-down counters are commonly used in the aerospace industry for fault detection thresholding. This paper applies the up-down counter technique to detect wind turbine faults. The thresholding problem involves a tradeoff between false alarms and missed detections. Counter based thresholding can detect smaller faults with higher probability and lower false alarms than is possible using simple constant thresholds. This improvement is achieved by effectively introducing dynamics into the thresholding logic as opposed to decisioning based on a single time step. Up down counters are applied to the development of a fault detection system for a commercial sized 4.8MW wind turbine. Realistic fault scenarios in the sensing, actuation and drivetrain subsystems are considered. It is seen that most faults can be detected with fast detection times and minimal false alarms without implementation of more complex filtering and detection techniques on residuals.

Robust Region-of-Attraction Estimation

We propose a method to compute invariant subsets of the region-of-attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty. Parameter-independent Lyapunov functions are used to characterize invariant subsets of the robust region-of-attraction. A branch-and-bound type refinement procedure reduces the conservatism. We demonstrate the method on an example from the literature and uncertain controlled short-period aircraft dynamics.

Stability Analysis With Dissipation Inequalities and Integral Quadratic Constraints

This technical note considers the stability of a feedback connection of a known linear, time-invariant system and a perturbation. The input/output behavior of the perturbation is described by an integral quadratic constraint (IQC). IQC stability theorems can be formulated in the frequency domain or with a time-domain dissipation inequality. The two approaches are connected by a non-unique factorization of the frequency domain IQC multiplier. The factorization must satisfy two properties for the dissipation inequality to be valid. First, the factorization must ensure the time-domain IQC holds for all finite times. Second, the factorization must ensure that a related matrix inequality, when feasible, has a positive semidefinite solution. This technical note shows that a class of frequency domain IQC multipliers has a factorization satisfying these two properties. Thus the dissipation inequality test, with an appropriate factorization, can be used with no additional conservatism.

New developments in sum of squares optimization and SOSTOOLS

We describe the latest additions to SOSTOOLS, a freely available MATLAB toolbox for formulating and solving sum of squares programs. Among the many improvements, there are native polynomial objects, structure-exploiting techniques for sparse and structured polynomials, new customized functions, and support for alternative SDP solvers. We sketch some of the theory behind the new improvements, and illustrate the new commands using control-oriented examples.