Computational complexity of μ calculation

The structured singular value μ measures the robustness of uncertain systems. Numerous researchers over the last decade have worked on developing efficient methods for computing μ. This paper considers the complexity of calculating μ with general mixed real/complex uncertainty in the framework of combinatorial complexity theory. In particular, it is proved that the μ recognition problem with either pure real or mixed real/complex uncertainty is NP-hard. This strongly suggests that it is futile to pursue exact methods for calculating μ of general systems with pure real or mixed uncertainty for other than small problems

Optimal co-design of control, scheduling and routing in multi-hop control networks

A Multi-hop Control Network consists of a plant where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. Given a SISO LTI plant, we will address the problem of co-designing a digital controller and the network parameters (scheduling and routing) in order to guarantee stability and maximize a performance metric on the transient response to a step input, with constraints on the control effort, on the output overshoot and on the bandwidth of the communication channel. We show that the above optimization problem is a polynomial optimization problem, which is generally NP-hard. We provide sufficient conditions on the network topology, scheduling and routing such that it is computationally feasible, namely such that it reduces to a convex optimization problem.Comment: 51st IEEE Conference on Decision and Control, 2012. Accepted for publication as regular pape

Deadbeat Robust Model Predictive Control: Robustness without Computing Robust Invariant Sets

Deadbeat Robust Model Predictive Control (DRMPC) is introduced as a new approach of Robust Model Predictive Control (RMPC) for linear systems with additive disturbances. Its main idea is to completely extinguish the effect of the disturbances in the predictions within a small number of time steps, called the deadbeat horizon. To this end, explicit deadbeat input sequences are calculated for the vertices of the disturbance set. They generalize to a nonlinear disturbance feedback policy for all disturbances by means of a barycentric function. Similar to previous approaches, this disturbance feedback policy can be either part of the online optimization (Online DRMPC) or pre-calculated during the design phase of the controller (Offline DRMPC). The main advantage over all other RMPC approaches is that no Robust Positive Invariant (RPI) set has to be calculated, which is often intractable for systems with higher dimensions. Nonetheless, for Online DRMPC and Offline DRMPC recursive feasibility and input-to-state stability can be guaranteed. A small numerical example compares the two versions of DRMPC and demonstrates that the performance of DRMPC is competitive with other state-of-the-art RMPC approaches. Its main advantage is its easy extension to linear time-varying (LTV) and linear parameter-varying (LPV) systems

Optimal ripple-free deadbeat controllers

A ripple-free deadbeat controller for a system exists if and only if there are no transmission zeros coinciding with the poles of the reference signal. Approaches to this problem often use the Diophantine equation solution. However, solutions provided by the Diophantine equation often exhibit extremely bad transient responses. This approach gives a new affine parametrization of solutions of the Diophantine equation. Based on this parametrization, LMI conditions are used to provide optimal or constrained controllers for design quantities such as overshoot, undershoot, control amplitude, 'slew rate' as well as for norm bounds such as l1, l2 and l infinity

An optimal controller based on linear approximation of an acoustical test facility, part B Final report

Optimal digital controller based on linear approximation of acoustical test facility, for determining effects of supersonic rocket engine noise on vehicle surfac

Constrained Finite Receding Horizon Linear Quadratic Control

Issues of feasibility, stability and performance are considered for a finite horizon formulation of receding horizon control (RHC) for linear systems under mixed linear state and control constraints. It is shown that for a sufficiently long horizon, a receding horizon policy will remain feasible and result in stability, even when no end constraint is imposed. In addition, offline finite horizon calculations can be used to determine not only a stabilizing horizon length, but guaranteed performance bounds for the receding horizon policy. These calculations are demonstrated on two examples