6,556 research outputs found
Optimal Universal Controllers for Roll Stabilization
Roll stabilization is an important problem of ship motion control. This
problem becomes especially difficult if the same set of actuators (e.g. a
single rudder) has to be used for roll stabilization and heading control of the
vessel, so that the roll stabilizing system interferes with the ship autopilot.
Finding the "trade-off" between the concurrent goals of accurate vessel
steering and roll stabilization usually reduces to an optimization problem,
which has to be solved in presence of an unknown wave disturbance. Standard
approaches to this problem (loop-shaping, LQG, -control etc.)
require to know the spectral density of the disturbance, considered to be a
\colored noise". In this paper, we propose a novel approach to optimal roll
stabilization, approximating the disturbance by a polyharmonic signal with
known frequencies yet uncertain amplitudes and phase shifts. Linear quadratic
optimization problems in presence of polyharmonic disturbances can be solved by
means of the theory of universal controllers developed by V.A. Yakubovich. An
optimal universal controller delivers the optimal solution for any uncertain
amplitudes and phases. Using Marine Systems Simulator (MSS) Toolbox that
provides a realistic vessel's model, we compare our design method with
classical approaches to optimal roll stabilization. Among three controllers
providing the same quality of yaw steering, OUC stabilizes the roll motion most
efficiently
Robust â„‹2 Performance: Guaranteeing Margins for LQG Regulators
This paper shows that ℋ2 (LQG) performance specifications can be combined with structured uncertainty in the system, yielding robustness analysis conditions of the same nature and computational complexity as the corresponding conditions for ℋ∞ performance. These conditions are convex feasibility tests in terms of Linear Matrix Inequalities, and can be proven to be necessary and sufficient under the same conditions as in the ℋ∞ case.
With these results, the tools of robust control can be viewed as coming full circle to treat the problem where it all began: guaranteeing margins for LQG regulators
Sparse Wide-Area Control of Power Systems using Data-driven Reinforcement Learning
In this paper we present an online wide-area oscillation damping control
(WAC) design for uncertain models of power systems using ideas from
reinforcement learning. We assume that the exact small-signal model of the
power system at the onset of a contingency is not known to the operator and use
the nominal model and online measurements of the generator states and control
inputs to rapidly converge to a state-feedback controller that minimizes a
given quadratic energy cost. However, unlike conventional linear quadratic
regulators (LQR), we intend our controller to be sparse, so its implementation
reduces the communication costs. We, therefore, employ the gradient support
pursuit (GraSP) optimization algorithm to impose sparsity constraints on the
control gain matrix during learning. The sparse controller is thereafter
implemented using distributed communication. Using the IEEE 39-bus power system
model with 1149 unknown parameters, it is demonstrated that the proposed
learning method provides reliable LQR performance while the controller matched
to the nominal model becomes unstable for severely uncertain systems.Comment: Submitted to IEEE ACC 2019. 8 pages, 4 figure
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach
In this article, we consider a receding horizon control of discrete-time
state-dependent jump linear systems, particular kind of stochastic switching
systems, subject to possibly unbounded random disturbances and probabilistic
state constraints. Due to a nature of the dynamical system and the constraints,
we consider a one-step receding horizon. Using inverse cumulative distribution
function, we convert the probabilistic state constraints to deterministic
constraints, and obtain a tractable deterministic receding horizon control
problem. We consider the receding control law to have a linear state-feedback
and an admissible offset term. We ensure mean square boundedness of the state
variable via solving linear matrix inequalities off-line, and solve the
receding horizon control problem on-line with control offset terms. We
illustrate the overall approach applied on a macroeconomic system
Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs
The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated
Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty
In this paper, we propose new sequential randomized algorithms for convex
optimization problems in the presence of uncertainty. A rigorous analysis of
the theoretical properties of the solutions obtained by these algorithms, for
full constraint satisfaction and partial constraint satisfaction, respectively,
is given. The proposed methods allow to enlarge the applicability of the
existing randomized methods to real-world applications involving a large number
of design variables. Since the proposed approach does not provide a priori
bounds on the sample complexity, extensive numerical simulations, dealing with
an application to hard-disk drive servo design, are provided. These simulations
testify the goodness of the proposed solution.Comment: 18 pages, Submitted for publication to IEEE Transactions on Automatic
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