Bo Bernhardsson

Stochastic analysis and control of real-time systems with random time delays

The paper discusses modeling and analysis of real-time systems subject to random time delays in the communication network. A new method for analysis of different control schemes is presented. The method is used to evaluate different suggested schemes from the literature. A new scheme, using so called timestamps, for handling the random time delays is then developed and successfully compared with previous schemes. The new scheme is based on stochastic control theory and a separation property is shown to hold for the optimal controller.

Comparison of Riemann and Lebesgue sampling for first order stochastic systems

The normal approach to digital control is to sample periodically in time. Using an analog of integration theory we can call this Riemann sampling. Lebesgue sampling or event based sampling is an alternative to Riemann sampling. It means that signals are sampled only when measurements pass certain limits. In this paper it is shown that Lebesgue sampling gives better performance for some simple systems.

Feedback–Feedforward Scheduling of Control Tasks

A scheduling architecture for real-time control tasks is proposed. The scheduler uses feedback from execution-time measurements and feedforward from workload changes to adjust the sampling periods of the control tasks so that the combined performance of the controllers is optimized. The performance of each controller is described by a cost function. Based on the solution to the optimal resource allocation problem, explicit solutions are derived for linear and quadratic approximations of the cost functions. It is shown that a linear rescaling of the nominal sampling frequencies is optimal for both of these approximations. An extensive inverted pendulum example is presented, where the performance obtained with open-loop, feedback, combined feedback and feedforward scheduling, and earliest-deadline first scheduling are compared. The performance under earliest-deadline first scheduling is explained by studying the behavior of periodic tasks under overload conditions. It is shown that the average values of the sampling periods equal the nominal periods, rescaled by the processor utilization.

A formula for computation of the real stability radius

This paper presents a readily computable formula for the real stability radius with respect to an arbitrary stability region in the complex plane.

Comparison of Periodic and Event Based Sampling for First-Order Stochastic Systems

Abstract Event based sampling is an alternative to traditional equidistant sampling. This means that signals are sampled only when measurements pass certain limits. Systems with event based sampling are much harder to analyze than systems with periodic sampling because the time varying nature of the closed loop system can not be avoided. In this paper we investigate some simple first order systems with event based sampling and compare achieved closed loop variance and sampling rate with results from periodic sampling. The analysis shows that event based sampling gives better performance than periodic sampling.

Analysis of real-time control systems with time delays

We discuss modeling and analysis of real-time control systems subject to random time delays in the communication network. A new method for analysis of given control schemes is presented. The state of the network is modeled by a Markov chain and Lyapunov equations for the expected LQG performance are presented. An example that illustrates the results is given.

Out of control because of harmonics-an analysis of the harmonic response of an inverter locomotive

Presents a method to use linear analysis to capture the frequency coupling of nonlinear and time-varying components. System stability is analyzed by connecting the harmonic transfer functions of the different component models. This facilitates an object-oriented approach to modeling, which supports reuse of models. An analysis of the complete railway system is, of course, difficult. Several locomotives can be moving along the power distribution line at the same time, and depending on the distance between them, the interaction changes. The power consumption also changes, depending on operating modes. During normal operation, energy is consumed from the network, but as modern locomotives use electrical braking, the power flow changes direction during deceleration, and energy is delivered back to the grid. The inverter trains are not passive systems. The converters are controlled with only limited system knowledge (local measurements of currents and voltages), making analysis and control design an even bigger challenge.

LQR optimization of linear system switching

Considers offline optimization of a switching sequence for a given finite set of linear control systems, together with joint optimization of control laws. A linear quadratic full information criterion is optimized and dynamic programming is used to find an optimal switching sequence and control law. The main result is a method for efficient pruning of the search tree to avoid combinatoric explosion. A method to prove optimality of a found candidate switch sequence and corresponding control laws is presented.

A Stabilizing Switching Scheme for Multi Controller Systems

The stability of a multi-controller system is analyzed using Lyapunov theory. Stability is guaranteed by a switching strategy determined by a combination of separate Lyapunov functions for the different controllers. The behavior on sliding surfaces is analyzed using non-smooth analysis according to Filippov. Two examples illustrate the theory.

LQG control over a Markov communication network

We formulate and solve a control problem where data are sent over a communication network that introduces random time delays. Past time delays are assumed known by the use of time stamps and the probability distribution of future delays are modeled with a Markov chain with continuous observation densities. We generalize previous results on LQG control of jump linear systems to cover this situation.