36,362 research outputs found
Adaptive Horizon Model Predictive Control and Al'brekht's Method
A standard way of finding a feedback law that stabilizes a control system to
an operating point is to recast the problem as an infinite horizon optimal
control problem. If the optimal cost and the optmal feedback can be found on a
large domain around the operating point then a Lyapunov argument can be used to
verify the asymptotic stability of the closed loop dynamics. The problem with
this approach is that is usually very difficult to find the optimal cost and
the optmal feedback on a large domain for nonlinear problems with or without
constraints. Hence the increasing interest in Model Predictive Control (MPC).
In standard MPC a finite horizon optimal control problem is solved in real time
but just at the current state, the first control action is implimented, the
system evolves one time step and the process is repeated. A terminal cost and
terminal feedback found by Al'brekht's methoddefined in a neighborhood of the
operating point is used to shorten the horizon and thereby make the nonlinear
programs easier to solve because they have less decision variables. Adaptive
Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon
length of Model Predictive Control (MPC) as needed. Its goal is to achieve
stabilization with horizons as small as possible so that MPC methods can be
used on faster and/or more complicated dynamic processes.Comment: arXiv admin note: text overlap with arXiv:1602.0861
Output-Feedback Control of Nonlinear Systems using Control Contraction Metrics and Convex Optimization
Control contraction metrics (CCMs) are a new approach to nonlinear control
design based on contraction theory. The resulting design problems are expressed
as pointwise linear matrix inequalities and are and well-suited to solution via
convex optimization. In this paper, we extend the theory on CCMs by showing
that a pair of "dual" observer and controller problems can be solved using
pointwise linear matrix inequalities, and that when a solution exists a
separation principle holds. That is, a stabilizing output-feedback controller
can be found. The procedure is demonstrated using a benchmark problem of
nonlinear control: the Moore-Greitzer jet engine compressor model.Comment: Conference submissio
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