74 research outputs found
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
A Hamilton-Jacobi-Bellman Approach to Ellipsoidal Approximations of Reachable Sets for Linear Time-Varying Systems
Reachable sets for a dynamical system describe collections of system states
that can be reached in finite time, subject to system dynamics. They can be
used to guarantee goal satisfaction in controller design or to verify that
unsafe regions will be avoided. However, general-purpose methods for computing
these sets suffer from the curse of dimensionality, which typically prohibits
their use for systems with more than a small number of states, even if they are
linear. In this paper, we demonstrate that viscosity supersolutions and
subsolutions of a Hamilton-Jacobi-Bellman equation can be used to generate,
respectively, under-approximating and over-approximating reachable sets for
time-varying nonlinear systems. Based on this observation, we derive dynamics
for a union and intersection of ellipsoidal sets that, respectively,
under-approximate and over-approximate the reachable set for linear
time-varying systems subject to an ellipsoidal input constraint and an
ellipsoidal terminal (or initial) set. We demonstrate that the dynamics for
these ellipsoids can be selected to ensure that their boundaries coincide with
the boundary of the exact reachable set along a solution of the system. The
ellipsoidal sets can be generated with polynomial computational complexity in
the number of states, making our approximation scheme computationally tractable
for continuous-time linear time-varying systems of relatively high dimension.Comment: 32 page
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