Joerg Raisch

Iterative Learning Control for Variable Pass Length Systems

Abstract Monotonic convergence of linear iterative learning control (ILC) systems with changing pass length is considered. The maximum pass length (MPL) error is introduced as a useful concept for convergence analysis of this class of systems. Using the lifted-system framework, a both necessary and sufficient monotonic convergence criterion is found for the 1-norm of the MPL error. Further findings on 2-norm and ∞-norm convergence are added. Finally, an example system is given, i.e. the control of an electrical stimulation system for gait assistance, and simulation results are provided.

On an Optimization Problem for a Class of Impulsive Hybrid Systems

This contribution addresses the problem of optimal control for a class of hybrid systems, where discrete transitions are accompanied by instantaneous changes in the continuous state variables, and where these changes can be considered as control variables. Based on a variational approach, necessary conditions of optimality are first established. The problem is then cast as a parametric optimization problem for which gradient information is derived. Finally, we discuss assumptions that guarantee convergence of a conceptual algorithm to a stationary solution. A brief discussion on the main implementation issues is also included.

Controllability of Second Order Leader-Follower Systems

Abstract In this paper we study formation control of a network of communicating mobile agents with double integrator dynamics. All agents run a consensus algorithm, several leader agents are further subject to an external input. We put this problem in a control theoretical framework and show that the controllability of the entire system via external control input depends only on the controllability of the follower system through the leaders. We then show necessary and sufficient conditions for the follower system to be controllable and relate the obtained conditions to the existing results on topological properties of the follower communication graph.

Minimax Model Predictive Operation Control of Microgrids

Abstract Due to the steady growth of decentralised distributed generation, the operational management of small, local electricity networks (microgrids) is becoming an increasing challenge to meet: How to provide an operational control for microgrids with a high share of renewable energy sources (RES) that is robust to perturbations? In this paper we address an optimal control problem (OCP) that maintains all of the stated properties in the presence of an uncertain load and RES infeed in islanded operation. Assuming that the uncertainty is within a bounded region along a given load and RES trajectory prediction, the problem is posed as a worst-case hybrid OCP, where the RES output can be curtailed. We propose a minimax (MM) model predictive control (MPC) scheme that adjusts according to the present uncertainty and can be formulated as a mixed-integer linear program (MILP) and solved numerically online.

Iterative learning control of drop foot stimulation with array electrodes for selective muscle activation

Disorders of the central nervous system like stroke often lead to a paresis of the muscles responsible for dorsiexion and eversion of the foot during swing phase. Functional electrical stimulation (FES) is commonly used to improve the foot movement. A precise placement of two single surface electrodes on the shank as well as a manual tuning of heel- switch triggered stimulation is required when using standard drop-foot stimulators. In this work, the use of automatically tuned array electrodes for selective nerve/muscle stimulation and the application of iterative learning control for adjusting stimulation intensities are investigated with the aim to obtain an optimal foot movement. The stimulation eect is observed by means of two inertial measurement units mounted on the foot and shank, respectively. Two array electrodes are placed over the areas covering the peroneal nerve and the muscle tibialis anterior. A fast identication procedure nds three suitable sets of array elements, forming so-called virtual electrodes, in both arrays. Two stimulation channels are established over the three virtual electrodes. Both channels produce dorsiexion, but one promotes eversion and the other inversion. A decoupling matrix is applied to the stimulation intensities of both channels in order to obtain independent control over dorsiexion and eversion. Finally, two independent iterative learning controllers are employed to achieve desired angle proles. The proposed stimulation and control scheme is initially tested on a healthy person sitting on a table with the shank and foot free to swing. A tracking RMS error of less than one degree is achieved within six walking steps.

Stability of synchronized motions of inverter-based microgrids under droop control

We consider the problems of frequency stability, voltage stability and power sharing in droop–controlled inverter–based microgrids with meshed topologies and dominantly inductive power lines. Assuming that the conductances in the microgrid can be neglected, a port–Hamiltonian description of a droop–controlled microgrid is derived. The model is used to establish sufficient conditions for local stability. Furthermore, we propose a condition for the controller parameters such that a desired steady–state active power distribution is achieved. The robustness of the stability condition with respect to the presence of conductances is analyzed via a simulation example based on the CIGRE benchmark medium voltage distribution network.

Modeling and Control for Max-Plus Systems with Partial Synchronization

A max-plus system with partial synchronization is a persistent discrete event system divided into a main subsystem and a secondary subsystem where some events in the secondary subsystem can only occur when (not after) associated events in the main subsystem occur. A formal model based on max-plus recursive equations is presented for max-plus systems with partial synchronization. Furthermore, the control problem of output tracking is addressed by assigning a higher priority to the main subsystem: the performance of the main subsystem is never degraded to improve the performance of the secondary subsystem. Two different control approaches are investigated: optimal feedforward control and model predictive control. In both cases, residuation theory is applied to efficiently solve the optimization problem.

Reducing an Operational Supervisory Control Problem by Decomposition for Deterministic Pushdown Automata

Abstract The purpose of Supervisory Control Theory (SCT) is to synthesize a controller for a plant and a specification such that the desired closed-loop behavior is enforced. Effective solvers have been constructed in the past for the setting of plants and specifications modeled by Deterministic Finite Automata (DFA). We extend the domain of the specification to Deterministic Pushdown Automata (DPDA) and verify an effective solver (up to two basic building blocks which ensure controllability and blockfreeness, effectively solved for this setting in two companion papers). We verify the enforcement of desired operational criteria, which are, in contrast to the setting of DFA, partly oblivious to the (un)marked language of the closed loop. Our general approach trivially covers the setting of DFA and can be reused and adapted to develop effective solvers for other settings as the realizability of solutions to the supervisory control problem (SCP) is considered on an Abstract: level.

Extending Supervisory Controller Synthesis to Deterministic Pushdown Automata Enforcing Controllability Least Restrictively

Abstract In this paper a step towards the generalization of supervisory control theory to situations where the specification is modeled by a deterministic pushdown automaton (DPDA) is provided. In particular, this paper presents an algorithm to calculate the largest controllable marked sublanguage of a given deterministic context free language (DCFL) by least restrictively removing controllability problems in a DPDA realization of this DCFL. It also provides a counterexample which shows that the algorithm by Griffin (2008) intended to solve the considered problem is not minimally restrictive.

ON SUBOPTIMAL CONTROL DESIGN FOR HYBRID AUTOMATA USING PREDICTIVE CONTROL TECHNIQUES

Abstract In this paper we propose an on-line design technique for the target control problem of hybrid automata. First, we compute off-line the shortest path, which has the minimum discrete cost, from an initial state to the given target set. Next, we derive a controller which successfully drives the system from the initial state to the target set while minimizing a cost function. The model predictive control (MPC) technique is used when the current state is not within a guard set, otherwise the mixed-integer predictive control (MIPC) technique is employed. An on-line, semi-explicit control algorithm is derived by combining the two techniques and applied on a high-speed and energy-saving control problem of the CPU processing.