Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis

In this paper, we extend the eigenvalue method of the algebraic Riccati equation to the differential Riccati equation (DRE) in contraction analysis. One of the main results is showing that solutions to the DRE can be expressed as functions of nonlinear eigenvectors of the differential Hamiltonian matrix. Moreover, under an assumption for the differential Hamiltonian matrix, real symmetricity, regularity, and positive semidefiniteness of solutions are characterized by nonlinear eigenvalues and eigenvectors

Stochastic Model Predictive Control Using Simplified Affine Disturbance Feedback for Chance-Constrained Systems

This letter covers the model predictive control of linear discrete-time systems subject to stochastic additive disturbances and chance constraints on their state and control input. We propose a simplified control parameterization under the framework of affine disturbance feedback, and we show that our method is equivalent to parameterization over the family of state feedback policies. Using our method, associated finite-horizon optimization can be computed efficiently, with a slight increase in conservativeness compared with conventional affine disturbance feedback parameterization

ParNMPC – a parallel optimisation toolkit for real-time nonlinear model predictive control

Real-time optimisation for nonlinear model predictive control (NMPC) has always been challenging, especially for fast-sampling and large-scale applications. This paper presents an efficient implementation of a highly parallelisable method for NMPC, called ParNMPC. The implementation details of ParNMPC are introduced, including a dedicated discretisation method suitable for parallelisation, a framework that unifies search direction calculation done using Newton's method and the parallel method, line search methods for guaranteeing convergence, and a warm start strategy for the interior-point method. To assess the performance of ParNMPC under different configurations, three experiments including a closed-loop simulation of a quadrotor, a real-world control example of a laboratory helicopter and a closed-loop simulation of a robot manipulator are shown. These experiments show the effectiveness and efficiency of ParNMPC both in serial and parallel

Efficient Riccati recursion for optimal control problems with pure-state equality constraints

A novel approach to efficiently treat pure-state equality constraints in optimal control problems (OCPs) using a Riccati recursion algorithm is proposed. The proposed method transforms a pure-state equality constraint into a mixed state-control constraint such that the constraint is expressed by variables at a certain previous time stage. It is showed that if the solution satisfies the second-order sufficient conditions of the OCP with the transformed mixed state-control constraints, it is a local minimum of the OCP with the original pure-state constraints. A Riccati recursion algorithm is derived to solve the OCP using the transformed constraints with linear time complexity in the grid number of the horizon, in contrast to a previous approach that scales cubically with respect to the total dimension of the pure-state equality constraints. Numerical experiments on the whole-body optimal control of quadrupedal gaits that involve pure-state equality constraints owing to contact switches demonstrate the effectiveness of the proposed method over existing approaches.Comment: 8 pages, 3 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Signal Temporal Logic Meets Convex-Concave Programming: A Structure-Exploiting SQP Algorithm for STL Specifications

This study considers the control problem with signal temporal logic (STL) specifications. Prior works have adopted smoothing techniques to address this problem within a feasible time frame and solve the problem by applying sequential quadratic programming (SQP) methods naively. However, one of the drawbacks of this approach is that solutions can easily become trapped in local minima that do not satisfy the specification. In this study, we propose a new optimization method, termed CCP-based SQP, based on the convex-concave procedure (CCP). Our framework includes a new robustness decomposition method that decomposes the robustness function into a set of constraints, resulting in a form of difference of convex (DC) program that can be solved efficiently. We solve this DC program sequentially as a quadratic program by only approximating the disjunctive parts of the specifications. Our experimental results demonstrate that our method has a superior performance compared to the state-of-the-art SQP methods in terms of both robustness and computational time.Comment: 8 pages, 5 figure

Relationships between vegetation types and soil properties along a topographical gradient on the northern coast of the Brgger Peninsula, Svalbard

Vegetation patterns in the high Arctic vary not only with proglacial chronosequence but also with a topographical gradient on older deglaciated areas which are covered by mature vegetation. A preliminary survey of local scale vegetation patterns along a topographical gradient with special reference to soil properties was conducted on the northern coast of the Brgger Peninsula, Svalbard in the high Arctic. Three community types of vascular plants were distinguished by common dominants: Cardamine type, Salix type and Oxyria/Luzula type. Each community type was comprised of different habitat types. The Cardamine type was restricted to near the bottom of depressions, where there was high soil water content. The Oxyria/Luzula type was characterized by habitats belonging to upper slopes to ridges, having high gravel content soils. On the other hand, the habitat preference of the Salix type, which had higher vegetation cover and biomass of vascular plants compared to the other two types, was not clear. The core habitat of fertile/undisturbed area, as described by the centrifugal community organization model, might be dominated by Salix polaris in this area. The other species had a refugium from interspecific competition in their preferred peripheral habitats such as exposed ridge or wetland

The methane flux along topographical gradients on a glacier foreland in the High Arctic, Ny-Alesund, Svalbard

In order to examine the relationship between the methane (CH_4) flux and soil factors and vegetation in High Arctic tundra, we investigated the CH_4 flux along topographical gradients on a glacier foreland in Ny-Alesund, Svalbard (79°N, 12°E). The CH4 flux rates varied widely among sites even within the same vegetation type, ranging from positive (emission) to negative (absorption) values. High CH_4 emission rates were detected on ridges and in sites with a low soil water content, but there was no significant relationship between CH_4 flux rates and soil factors including soil moisture, pH, soil carbon and nitrogen content. Mean values of CH_4 emission and CH_4 absorption were 0.30±0.33 mg m^(-2) h^(-1) (n=12) and 0.11±0.06 mg m^(-2) h^(-1) (n=11), respectively. These findings suggest that the study area is a small source of CH_4 with a mean flux of 0.11 mg CH_4 m^(-2) h^(-1) (0.083 mg C m^(-2) h^(-1)). It was concluded that carbon flux derived from CH_4 accounts for an extremely small proportion of the total carbon flux from soil in this area

Online-Computation Approach to Optimal Control of Noise-Affected Nonlinear Systems with Continuous State and Control Spaces

A novel online-computation approach to optimal control of nonlinear, noise-affected systems with continuous state and control spaces is presented. In the proposed algorithm, system noise is explicitly incorporated into the control decision. This leads to superior results compared to state-of-the-art nonlinear controllers that neglect this influence. The solution of an optimal nonlinear controller for a corresponding deterministic system is employed to find a meaningful state space restriction. This restriction is obtained by means of approximate state prediction using the noisy system equation. Within this constrained state space, an optimal closed-loop solution for a finite decisionmaking horizon (prediction horizon) is determined within an adaptively restricted optimization space. Interleaving stochastic dynamic programming and value function approximation yields a solution to the considered optimal control problem. The enhanced performance of the proposed discrete-time controller is illustrated by means of a scalar example system. Nonlinear model predictive control is applied to address approximate treatment of infinite-horizon problems by the finite-horizon controller