State feedback policies for robust receding horizon control: uniqueness, continuity, and stability

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Offset-free control of constrained linear discrete-time systems subject to persistent unmeasured disturbances

This paper addresses the design of a dynamic, nonlinear, time-invariant, state feedback controller that guarantees constraint satisfaction and offset-free control in the presence of unmeasured, persistent, non-stationary, additive disturbances. First, this objective is obtained by designing a dynamic, linear, time-invariant, offset-free controller, and an appropriate domain of attraction for this linear controller is denned. Following this, the linear (unconstrained) control input is modified by adding a perturbation term that is computed by a robust receding horizon controller. It is shown that the domain of attraction of the receding horizon controller contains that of the linear controller, and an efficient implementation of the receding horizon controller is proposed.Published versio

Move blocking strategies in receding horizon control

Abstract — In order to deal with the computational burden of optimal control, it is common practice to reduce the degrees of freedom by fixing the input or its derivatives to be constant over several time-steps. This policy is referred to as “move blocking”. This paper will address two issues. First, a survey of various move blocking strategies is presented and the shortcomings of these blocking policies, such as the lack of stability and constraint satisfaction guarantees, will be illustrated. Second, a novel move blocking scheme, “Moving Window Blocking” (MWB), will be presented. In MWB, the blocking strategy is time-dependent such that the scheme yields stability and feasibility guarantees for the closed-loop system. Finally, the results of a large case-study are presented that illustrate the advantages and drawbacks of the various control strategies discussed in this paper

Reliable solution to dynamic optimization problems using integrated residual regularized direct collocation

Direct collocation (DC) is a widely used method for solving dynamic optimization problems (DOPs), but its implementation simplicity and computational efficiency are limited for challenging problems. For DOPs involving singular arcs, DC solutions often exhibit significant fluctuations along the singular arc, accompanied by large residual errors between collocation points, where the dynamic constraints are enforced as equality constraints. In this paper, we introduce the direct transcription method of integrated residual regularized direct collocation (IRRDC). This approach enforces dynamic constraints using a combination of point-wise residual constraints (expressed as either equalities or inequalities) and a penalty term on the integrated residual error, which helps reduce errors between collocation points. IRRDC retains the implementation simplicity of DC while improving both solution accuracy and efficiency, particularly for challenging problem types. Through the examples, we demonstrate that for problems where traditional DC results in excessive fluctuations, IRRDC effectively suppresses fluctuations and yields solutions with greater accuracy — at least two orders of magnitude lower in various error measures in relation to the dynamic and path constraints

Search of the Orion spur for continuous gravitational waves using a loosely coherent algorithm on data from LIGO interferometers

We report results of a wideband search for periodic gravitational waves from isolated neutron stars within the Orion spur towards both the inner and outer regions of our Galaxy. As gravitational waves interact very weakly with matter, the search is unimpeded by dust and concentrations of stars. One search disk (A) is 6.87° in diameter and centered on 20h10m54.71s+33°33′25.29′′, and the other (B) is 7.45° in diameter and centered on 8h35m20.61s-46°49′25.151′′. We explored the frequency range of 50-1500 Hz and frequency derivative from 0 to -5×10-9 Hz/s. A multistage, loosely coherent search program allowed probing more deeply than before in these two regions, while increasing coherence length with every stage. Rigorous follow-up parameters have winnowed the initial coincidence set to only 70 candidates, to be examined manually. None of those 70 candidates proved to be consistent with an isolated gravitational-wave emitter, and 95% confidence level upper limits were placed on continuous-wave strain amplitudes. Near 169 Hz we achieve our lowest 95% C.L. upper limit on the worst-case linearly polarized strain amplitude h0 of 6.3×10-25, while at the high end of our frequency range we achieve a worst-case upper limit of 3.4×10-24 for all polarizations and sky locations. © 2016 American Physical Society

Optimal control of constrained, piecewise affine systems with bounded disturbances

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Designing model predictive controllers with prioritised constraints and objectives

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