Karl Worthmann

Analysis of Unconstrained Nonlinear MPC Schemes with Time Varying Control Horizon

For nonlinear discrete time systems satisfying a controllability condition, we present a stability condition for model predictive control without stabilizing terminal constraints or costs. The condition is given in terms of an analytical formula which can be employed in order to determine a prediction horizon length for which asymptotic stability or a performance guarantee is ensured. Based on this formula a sensitivity analysis with respect to the prediction and the possibly time varying control horizon is carried out.

Distributed and Decentralized Control of Residential Energy Systems Incorporating Battery Storage

The recent rapid uptake of residential solar photovoltaic installations provides many challenges for electricity distribution networks designed for one-way power flow from the generator to residential customers via transmission and distribution networks. For grid-connected installations, large amounts of generation during low load periods or intermittent generation can lead to a difficulty in balancing supply and demand, maintaining voltage and frequency stability, and may even result in outages due to overvoltage conditions tripping protection circuits. In this paper, we present four control methodologies to mitigate these difficulties using small-scale distributed battery storage. These four approaches represent three different control architectures: 1) centralized; 2) decentralized; and 3) distributed control. These approaches are validated and compared using data on load and generation profiles from customers in an Australian electricity distribution network.

AN EXPONENTIAL TURNPIKE THEOREM FOR DISSIPATIVE DISCRETE TIME OPTIMAL CONTROL PROBLEMS

We investigate the exponential turnpike property for finite horizon undiscounted discrete time optimal control problems without any terminal constraints. Considering a class of strictly dissipative systems, we derive a boundedness condition for an auxiliary optimal value function which implies the exponential turnpike property. Two theorems illustrate how this boundedness condition can be concluded from structural properties like controllability and stabilizability of the control system under consideration.

Brief paper: Continuous-time controller redesign for digital implementation: A trajectory based approach

Given a continuous-time nonlinear closed loop system, we investigate sampled-data feedback laws for which the trajectories of the sampled-data closed loop system converge to the continuous-time trajectories with a prescribed rate of convergence as the length of the sampling interval tends to zero. We derive necessary and sufficient conditions for the existence of such sampled-data feedback laws and-in case of existence-provide explicit redesign formulas and algorithms for these controllers.

A prediction based control scheme for networked systems with delays and packet dropouts

We present a networked control scheme which uses a model based prediction and time-stamps in order to compensate for delays and packet dropouts in the transmission between sensor and controller and between controller and actuator, respectively. In order to analyze the properties of our scheme, we introduce the notion of prediction consistency which enables us to precisely state the network properties needed in order to ensure stability of the closed loop.

Stability and Feasibility of State Constrained MPC without Stabilizing Terminal Constraints

Abstract In this paper we investigate stability and recursive feasibility of a nonlinear receding horizon control scheme without terminal constraints and costs but imposing state and control constraints. Under a local controllability assumption we show that every level set of the infinite horizon optimal value function is contained in the basin of attraction of the asymptotically stable equilibrium for sufficiently large optimization horizon N . For stabilizable linear systems we show the same for any compact subset of the interior of the viability kernel. Moreover, estimates for the necessary horizon length N are given via an analysis of the optimal value function at the boundary of the viability kernel.

Receding horizon optimal control for the wave equation

We present a receding horizon optimal control approach for the one-dimensional linear wave equation. In order to prove stability and suboptimality of this approach we use a weighted energy as cost functional. Furthermore, we apply similar methods to a semilinear parabolic equation.

A Distributed NMPC Scheme without Stabilizing Terminal Constraints

We consider a distributed NMPC scheme in which the individual systems are coupled via state constraints. In order to avoid violation of the constraints, the subsystems communicate their individual predictions to the other subsystems once in each sampling period. For this setting, Richards and How have proposed a sequential distributed MPC formulation with stabilizing terminal constraints. In this chapter we show how this scheme can be extended to MPC without stabilizing terminal constraints or costs.We show theoretically and by means of numerical simulations that under a suitable controllability condition stability and feasibility can be ensured even for rather short prediction horizons.

Model Predictive Control of Nonholonomic Mobile Robots Without Stabilizing Constraints and Costs

The problem of steering a nonholonomic mobile robot to a desired position and orientation is considered. In this paper, a model predictive control (MPC) scheme based on tailored nonquadratic stage cost is proposed to fulfill this control task. We rigorously prove asymptotic stability while neither stabilizing constraints nor costs are used. To this end, we first design suitable maneuvers to construct bounds on the value function. Second, these bounds are exploited to determine a prediction horizon length such that the asymptotic stability of the MPC closed loop is guaranteed. Finally, numerical simulations are conducted to explain the necessity of having nonquadratic running costs.

The Role of Sampling for Stability and Performance in Unconstrained Nonlinear Model Predictive Control

We investigate the impact of sampling on stability and performance estimates in nonlinear model predictive control without stabilizing terminal constraints or costs. Interpreting the sampling period as a discretization parameter, the relation between continuous and discrete time estimates depending on this parameter is analyzed. The technique presented in this paper allows us to determine the sampling rate required in order to approximate the continuous time suboptimality bound arbitrarily well and, thus, gives insight into the trade-off between sampling time and guaranteed performance.