Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational resource is the underlying design consideration. This paper analyzes the MPC design problem with control performance and required computational resource as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational resource separately -- often with the latter as a fixed constraint -- which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient solver are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the design approach and importance of the developed conditions for an effective solver of the MOD-MPC problem

Sub-Optimal Moving Horizon Estimation in Feedback Control of Linear Constrained Systems

Moving horizon estimation (MHE) offers benefits relative to other estimation approaches by its ability to explicitly handle constraints, but suffers increased computation cost. To help enable MHE on platforms with limited computation power, we propose to solve the optimization problem underlying MHE sub-optimally for a fixed number of optimization iterations per time step. The stability of the closed-loop system is analyzed using the small-gain theorem by considering the closed-loop controlled system, the optimization algorithm dynamics, and the estimation error dynamics as three interconnected subsystems. By assuming incremental input/output-to-state stability ({\delta}- IOSS) of the system and imposing standard ISS conditions on the controller, we derive conditions on the iteration number such that the interconnected system is input-to-state stable (ISS) w.r.t. the external disturbances. A simulation using an MHE- MPC estimator-controller pair is used to validate the results.Comment: 6 page journal paper with 2 figure

Auction algorithm sensitivity for multi-robot task allocation

We consider the problem of finding a low-cost allocation and ordering of tasks between a team of robots in a d-dimensional, uncertain, landscape, and the sensitivity of this solution to changes in the cost function. Various algorithms have been shown to give a 2-approximation to the MinSum allocation problem. By analysing such an auction algorithm, we obtain intervals on each cost, such that any fluctuation of the costs within these intervals will result in the auction algorithm outputting the same solution

Asynchronous Event-Triggered Control for Non-Linear Systems

With the increasing ubiquity of networked control systems, various strategies for sampling constituent subsystems' outputs have emerged. In contrast with periodic sampling, event-triggered control provides a way to efficiently sample a subsystem and conserve network resource usage, by triggering an update only when a state-dependent error threshold is satisfied. Herein we describe a scheme for asynchronous event-triggered control (ETC) of a nonlinear plant using sampler subsystems with hybrid dynamics. By exploiting inherent differences in the plant and controllers time scales, the proposed scheme permits independent sampling of plant and controller states. We extend existing ETC literature by adopting a more general representation of the sampler subsystem dynamics, thus accommodating different sampling schemes for both synchronous and asynchronous ETC applications. We present a numerical example in order to illustrate important operational considerations for the proposed scheme