arXiv subjects

Ian R. Manchester

Publications and source records attributed to Ian R. Manchester.

At least 73 records · Page 4Linked to original sources

arXiv2020

A Comparison of LPV Gain Scheduling and Control Contraction Metrics for Nonlinear Control

Gain-scheduled control based on linear parameter-varying (LPV) models derived from local linearizations is a widespread nonlinear technique for tracking time-varying setpoints. Recently, a nonlinear control scheme based on Control Contraction Metrics (CCMs) has been developed to track arbitrary admissible trajectories. This paper presents a comparison study of these two approaches. We show that the CCM based approach is an extended gain-scheduled control scheme which achieves global reference-independent stability and performance through an exact control realization which integrates a series of local LPV controllers on a particular path between the current and reference states.

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arXiv2020

Sparse Resource Allocation for Control of Spreading Processes via Convex Optimization

In this letter we propose a method for sparse allocation of resources to control spreading processes -- such as epidemics and wildfires -- using convex optimization, in particular exponential cone programming. Sparsity of allocation has advantages in situations where resources cannot easily be distributed over a large area. In addition, we introduce a model of risk to optimize the product of the likelihood and the future impact of an outbreak. We demonstrate with a simplified wildfire example that our method can provide more targeted resource allocation compared to previous approaches based on geometric programming.

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arXiv2020

Path following of a class of underactuated mechanical systems via immersion and invariance-based orbital stabilization

This paper aims to provide a new problem formulation of path following for mechanical systems without time parameterization nor guidance laws, namely, we express the control objective as an orbital stabilization problem. It is shown that, it is possible to adapt the immersion and invariance technique to design static state-feedback controllers that solve the problem. In particular, we select the target dynamics adopting the recently introduced Mexican sombrero energy assignment method. To demonstrate the effectiveness of the proposed method we apply it to control underactuated marine surface vessels.

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arXiv2019

Contracting Implicit Recurrent Neural Networks: Stable Models with Improved Trainability

Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an implicit model structure that allows for a convex parametrization of stable models using contraction analysis of non-linear systems. Using these stability conditions we propose a new approach to model initialization and then provide a number of empirical results comparing the performance of our proposed model set to previous stable RNNs and vanilla RNNs. By carefully controlling stability in the model, we observe a significant increase in the speed of training and model performance.

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arXiv2019

Continuous-time Dynamic Realization for Nonlinear Stabilization via Control Contraction Metrics

Nonlinear stabilization using control contraction metric (CCM) method usually involves an online optimization problem to compute a minimal geodesic (a shortest path) between pair of states, which is not desirable for real-time applications. This paper introduces a continuous-time dynamic realization which distributes the computational cost of the optimization problem over the time domain. The basic idea is to force the internal state of the dynamic controller to converge to a geodesic using covariant derivative information. A numerical example illustrates the proposed approach.

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arXiv2019

Priority Maps for Surveillance and Intervention of Wildfires and other Spreading Processes

Unmanned Aerial Vehicle (UAV) path planning algorithms often assume a knowledge reward function or priority map, indicating the most important areas to visit. In this paper we propose a method to create priority maps for monitoring or intervention of dynamic spreading processes such as wildfires. The presented optimization framework utilizes the properties of positive systems, in particular the separable structure of value (cost-to-go) functions, to provide scalable algorithms for surveillance and intervention. We present results obtained for a 16 and 1000 node example and convey how the priority map responds to changes in the dynamics of the system. The larger example of 1000 nodes, representing a fictional landscape, shows how the method can integrate bushfire spreading dynamics, landscape and wind conditions. Finally, we give an example of combining the proposed method with a travelling salesman problem for UAV path planning for wildfire intervention.

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arXiv2019

Robust Contraction Analysis of Nonlinear Systems via Differential IQC

We present a new approach to verifying contraction and $L_2$-gain of uncertain nonlinear systems, extending the well-known method of integral quadratic constraints. The uncertain system consists of a feedback interconnection of a nonlinear nominal system and uncertainties satisfying differential integral quadratic constraints. A pointwise linear matrix inequality condition is formulated to verify the closed-loop differential $ L_2 $ gain, which can lead to global reference-independent $ L_2 $ gain performance of the nonlinear uncertain system. For a polynomial nominal system, the convex verification conditions can be solved via sum-of-squares programming. A simple computational example based on jet-engine surge with input delays illustrates the approach.

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arXiv2019

Dynamical Privacy in Distributed Computing -- Part I: Privacy Loss and PPSC Mechanism

A distributed computing protocol consists of three components: (i) Data Localization: a network-wide dataset is decomposed into local datasets separately preserved at a network of nodes; (ii) Node Communication: the nodes hold individual dynamical states and communicate with the neighbors about these dynamical states; (iii) Local Computation: state recursions are computed at each individual node. Information about the local datasets enters the computation process through the node-to-node communication and the local computations, which may be leaked to dynamics eavesdroppers having access to global or local node states. In this paper, we systematically investigate this potential computational privacy risks in distributed computing protocols in the form of structured system identification, and then propose and thoroughly analyze a Privacy-Preserving-Summation-Consistent (PPSC) mechanism as a generic privacy encryption subroutine for consensus-based distributed computations. The central idea is that the consensus manifold is where we can both hide node privacy and achieve computational accuracy. In this first part of the paper, we demonstrate the computational privacy risks in distributed algorithms against dynamics eavesdroppers and particularly in distributed linear equation solvers, and then propose the PPSC mechanism and illustrate its usefulness.

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arXiv2018

Distributed Nonlinear Control Design using Separable Control Contraction Metrics

This paper gives convex conditions for synthesis of a distributed control system for large-scale networked nonlinear dynamic systems. It is shown that the technique of control contraction metrics (CCMs) can be extended to this problem by utilizing separable metric structures, resulting in controllers that only depend on information from local sensors and communications from immediate neighbours. The conditions given are pointwise linear matrix inequalities, and are necessary and sufficient for linear positive systems and certain monotone nonlinear systems. Distributed synthesis methods for systems on chordal graphs are also proposed based on SDP decompositions. The results are illustrated on a problem of vehicle platooning with heterogeneous vehicles, and a network of nonlinear dynamic systems with over 1000 states that is not feedback linearizable and has an uncontrollable linearization

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arXiv2018

Control Contraction Metrics on Finsler Manifolds

Control Contraction Metrics (CCMs) provide a nonlinear controller design involving an offline search for a Riemannian metric and an online search for a shortest path between the current and desired trajectories. In this paper, we generalize CCMs to Finsler geometry, allowing the use of non-Riemannian metrics. We provide open loop and sampled data controllers. The sampled data control construction presented here does not require real time computation of globally shortest paths, simplifying computation.

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arXiv2018

Specialized Interior Point Algorithm for Stable Nonlinear System Identification

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation fidelity and guarantee stability via semidefinite programming (SDP), however the resulting SDPs have large dimension, limiting their utility in practical problems. In this paper we develop a path-following interior point algorithm that takes advantage of special structure in the problem and reduces computational complexity from cubic to linear growth with the length of the data set. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, and we demonstrate superior generalization to new data. We also explore the "regularizing" effect of stability constraints as an alternative to regressor subset selection.

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arXiv2017

An Amendment to "Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design"

We provide an amendment to the first theorem of "Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design" by Manchester & Slotine in the form of an additional technical condition required to show integrability of differential control signals. This technical condition is shown to be satisfied under the original assumptions if the input matrix is constant rank, and also if the strong conditions for a CCM hold. However a simple counterexample shows that if the input matrix drops rank, then the weaker conditions of the original theorem may not imply stabilizability of all trajectories. The remaining claims and illustrative examples of the paper are shown to remain valid with the new condition.

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arXiv2017

Contracting Nonlinear Observers: Convex Optimization and Learning from Data

A new approach to design of nonlinear observers (state estimators) is proposed. The main idea is to (i) construct a convex set of dynamical systems which are contracting observers for a particular system, and (ii) optimize over this set for one which minimizes a bound on state-estimation error on a simulated noisy data set. We construct convex sets of continuous-time and discrete-time observers, as well as contracting sampled-data observers for continuous-time systems. Convex bounds for learning are constructed using Lagrangian relaxation. The utility of the proposed methods are verified using numerical simulation.

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arXiv2017

Nonlinear Stabilization via Control Contraction Metrics: a Pseudospectral Approach for Computing Geodesics

Real-time nonlinear stabilization techniques are often limited by inefficient or intractable online and/or offline computations, or a lack guarantee for global stability. In this paper, we explore the use of Control Contraction Metrics (CCM) for nonlinear stabilization because it offers tractable offline computations that give formal guarantees for global stability. We provide a method to solve the associated online computation for a CCM controller - a pseudospectral method to find a geodesic. Through a case study of a stiff nonlinear system, we highlight two key benefits: (i) using CCM for nonlinear stabilization and (ii) rapid online computations amenable to real-time implementation. We compare the performance of a CCM controller with other popular feedback control techniques, namely the Linear Quadratic Regulator (LQR) and Nonlinear Model Predictive Control (NMPC). We show that a CCM controller using a pseudospectral approach for online computations is a middle ground between the simplicity of LQR and stability guarantees for NMPC.

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arXiv2017

On Existence of Separable Contraction Metrics for Monotone Nonlinear Systems

Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are exponentially stable, can have that property verified by a separable metric. Making use of recent results in the theory of positive linear systems and separable Lyapunov functions, we prove several new results showing when this is possible, and discuss the application of to nonlinear distributed control design via convex optimization.

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arXiv2017

Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design

We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control system. The conditions have a simple geometrical interpretation, can be written as a convex feasibility problem, and are invariant under coordinate changes. We show that these conditions are necessary and sufficient for feedback linearizable systems, and also derive novel convex criteria for exponential stabilization of a nonlinear submanifold of state space. We illustrate the benefits of convexity by constructing a controller for an unstable polynomial system that combines local optimality and global stability, using a metric found via sum-of-squares programming.

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arXiv2017

Convex Parameterizations and Fidelity Bounds for Nonlinear Identification and Reduced-Order Modelling

Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error minimization, leads to optimization problems that are generally non-convex in the model parameters and suffer from multiple local minima. In this work we present methods which address these problems through convex optimization, based on Lagrangian relaxation, dissipation inequalities, contraction theory, and semidefinite programming. We demonstrate the proposed methods with a model order reduction task for electronic circuit design and the identification of a pneumatic actuator from experiment.

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arXiv2016

Decentralized Nonlinear Feedback Design with Separable Control Contraction Metrics

The problem under consideration is the synthesis of a distributed controller for a nonlinear network composed of input affine systems. The objective is to achieve exponential convergence of the solutions. To design such a feedback law, methods based on contraction theory are employed to render the controller-synthesis problem scalable and suitable to use distributed optimization. The nature of the proposed approach is constructive, because the computation of the desired feedback law is obtained by solving a convex optimization problem. An example illustrates the proposed methodology.

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