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One typical approach to implement model predictive control in relatively fast sample rate applications utilises linearised plant models to simplify the online optimisation problem in the presence of limited computation budget. A number of linearisation points may be used to account for the variation in the non-linear plant over the entire operating domain, leading to potential switched linear time-invariant (LTI) or linear time-variant (LTV) implementations. The choice of these linearisation points, and the regions over which they are considered valid, can have a significant impact on the closed loop performance of the overall controller. In this work, in the presence of a high-fidelity digital twin of a non-linear plant, a numerical algorithm for the selection of linearisation points is proposed. The approach makes use of the concept of disturbance sets to determine both the linearisation points and the domain to which each linearisation point applies. The use of disturbance sets provides an implicit connection to closed-loop controller performance if robust model predictive control algorithms are implemented. The proposed approach is implemented for the challenging problem of diesel air-path control, with simulation results on a high-fidelity mean value engine model used to demonstrate the efficacy of the approach. [ABSTRACT FROM AUTHOR]

Abstract The paper considers a problem of detecting and mitigating biasing attacks on networks of state observers targeting cooperative state estimation algorithms. The problem is cast within the recently developed framework of distributed estimation utilizing the vector dissipativity approach. The paper shows that a network of distributed observers can be endowed with an additional attack detection layer capable of detecting biasing attacks and correcting their effect on estimates produced by the network. An example is provided to illustrate the performance of the proposed distributed attack detector. [ABSTRACT FROM AUTHOR]

Among first order optimization methods, Polyak's heavy ball method has long been known to guarantee the asymptotic rate of convergence matching Nesterov's lower bound for functions defined in an infinite-dimensional space. In this paper, we use results on the robust gain margin of linear uncertain feedback control systems to show that the heavy ball method is provably worst-case asymptotically optimal when applied to quadratic functions in a finite dimensional space. [ABSTRACT FROM AUTHOR]

We study numerical optimization algorithms that use zeroth-order information to minimize time-varying geodesically convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of attention in both the time-varying and time-invariant cases. However, the extension to Riemannian manifolds is much less developed. We focus on Hadamard manifolds, which are a special class of Riemannian manifolds with global nonpositive curvature that offer convenient grounds for the generalization of convexity notions. Specifically, we derive bounds on the expected instantaneous tracking error, and we provide algorithm parameter values that minimize the algorithm's performance. Our results illustrate how the manifold geometry in terms of the sectional curvature affects these bounds. Additionally, we provide dynamic regret bounds for this online optimization setting. To the best of our knowledge, these are the first regret bounds even for the Euclidean version of the problem. Lastly, via numerical simulations, we demonstrate the applicability of our algorithm on an online Karcher mean problem. [ABSTRACT FROM AUTHOR]

This paper concerns the verification of continuous-time polynomial spline trajectories against linear temporal logic specifications (LTL without 'next'). Each atomic proposition is assumed to represent a state space region described by a multivariate polynomial inequality. The proposed approach samples a trajectory strategically, to capture every one of its region transitions. This yields a discrete word called a trace, which is amenable to established formal methods for path checking. The original continuous-time trajectory is shown to satisfy the specification if and only if its trace does. General topological conditions on the sample points are derived that ensure a trace is recorded for arbitrary continuous paths, given arbitrary region descriptions. Using techniques from computer algebra, a trace generation algorithm is developed to satisfy these conditions when the path and region boundaries are defined by polynomials. The proposed PolyTrace algorithm has polynomial complexity in the number of atomic propositions, and is guaranteed to produce a trace of any polynomial path. Its performance is demonstrated via numerical examples and a case study from robotics. [ABSTRACT FROM AUTHOR]

For industrial contouring and machining applications such as laser cutting, it is desirable to be able to bound errors without unduly compromising machine throughput. Traditional control architectures in machining are unable to explicitly bound tracking errors, and therefore, conservative operation is required to ensure satisfactory performance of the overall system. This is particularly relevant in contouring applications when the end effector is connected to the drive via a flexible link, and no direct feedback measurement about the end-effector position is available. In this article, a model predictive approach is proposed, which guarantees that a desired level of tracking error is met for the case where the structure is flexible and the end-effector position is estimated. To achieve this, a robust control invariant set is estimated using a computationally tractable algorithm and incorporated into the problem formulation. The applicability of the proposed approach is successfully demonstrated via simulation and experiments conducted on a commercial single axis system. [ABSTRACT FROM AUTHOR]

Constrained finite-horizon linear-quadratic optimal control problems are studied within the context of discrete-time dynamics that arise from the series interconnection of subsystems. A structured algorithm is devised for computing the Newton-like steps of primal-dual interior-point methods for solving a particular re-formulation of the problem as a quadratic program. This algorithm has the following properties: (i) the computation cost scales linearly in the number of subsystems along the cascade; and (ii) the computations can be distributed across a linear processor network, with localised problem data dependencies between the processor nodes and low communication overhead. The computation cost of the approach, which is based on a fixed permutation of the primal and dual variables, scales cubically in the time horizon of the original optimal control problem. Limitations in these terms are explored as part of a numerical example. This example involves application of the main results to model data for the cascade dynamics of an automated irrigation channel in particular. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimisation of a time varying scalar field by a network of agents with no gradient information. We propose a composite control law, blending extremum seeking with formation control in order to converge to the extrema faster by minimising the gradient estimation error. By formalising the relationship between the formation and the gradient estimation error, we provide a novel analysis to prove the convergence of the network to a bounded neighbourhood of the field's time varying extrema. We assume the time-varying field satisfies the Polyak–Łojasiewicz inequality and the gradient is Lipschitz continuous at each iteration. Numerical studies and comparisons are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

Robust autonomy stacks require tight integration of perception, motion planning, and control layers, but these layers often inadequately incorporate inherent perception and prediction uncertainties, either ignoring them altogether or making questionable assumptions of Gaussianity. Robots with nonlinear dynamics and complex sensing modalities operating in an uncertain environment demand more careful consideration of how uncertainties propagate across stack layers. We propose a framework to integrate perception, motion planning, and control by explicitly incorporating perception and prediction uncertainties into planning so that risks of constraint violation can be mitigated. Specifically, we use a nonlinear model predictive control based steering law coupled with a decorrelation scheme based Unscented Kalman Filter for state and environment estimation to propagate the robot state and environment uncertainties. Subsequently, we use distributionally robust risk constraints to limit the risk in the presence of these uncertainties. Finally, we present a layered autonomy stack consisting of a nonlinear steering-based distributionally robust motion planning module and a reference trajectory tracking module. Our numerical experiments with nonlinear robot models and an urban driving simulator show the effectiveness of our proposed approaches. [ABSTRACT FROM AUTHOR]

Solving the Lexicographic Bottleneck Assignment Problem (LexBAP) typically relies on centralised computation with order O (n 4) complexity. We consider the Sequential Bottleneck Assignment Problem (SeqBAP), which yields a greedy solution to the LexBAP and discuss the relationship between the SeqBAP, the LexBAP, and the Bottleneck Assignment Problem (BAP). In particular, we reexamine tools used to analyse the structure of the BAP, and apply them to derive an O (n 3) algorithm that solves the SeqBAP. We show that the set of solutions of the LexBAP is a subset of the solutions of the SeqBAP and analyse the conditions for which the solutions sets are identical. Furthermore, we provide a method to verify the satisfaction of these conditions. In cases where the conditions are satisfied, the proposed algorithm for solving the SeqBAP solves the LexBAP with computation that has lower complexity and can be distributed over a network of computing agents. The applicability of the approach is demonstrated with a case study where mobile robots are assigned to goal locations. [ABSTRACT FROM AUTHOR]

Advanced manufacturing is characterised by machines that move an end effector through a given trajectory to perform operations such as cutting, grinding and printing. In many industrial machines, properties such as structural flexibility, external disturbances as well as spatially separate actuator and end effector make the tracking problem challenging. In this paper, a literature survey on trajectory tracking control algorithms is conducted to examine representative features of existing methods. Then the major classes of algorithms are compared on a commercial single-axis test bench to provide practitioners with a direct insight into the trade-off between performance and implementation. • Representative features of existing tracking control algorithms are examined. • Trade-off of controllers between performance and implementation effort is discussed. • A direct insight into the trade-offs is provided based on the experiments. [ABSTRACT FROM AUTHOR]

This paper is about an encryption based approach to the secure implementation of feedback controllers for physical systems. Specifically, Paillier's homomorphic encryption is used to digitally implement a class of linear dynamic controllers, which includes the commonplace static gain and PID type feedback control laws as special cases. The developed implementation is amenable to Field Programmable Gate Array (FPGA) realization. Experimental results, including timing analysis and resource usage characteristics for different encryption key lengths, are presented for the realization of an inverted pendulum controller; as this is an unstable plant, the control is necessarily fast. [ABSTRACT FROM AUTHOR]

In this paper, we analyse two-player games by their response graphs. The response graph has nodes which are strategy profiles, with an arc between profiles if they differ in the strategy of a single player, with the direction of the arc indicating the preferred option for that player. Response graphs, and particularly their sink strongly connected components, play an important role in modern techniques in evolutionary game theory and multi-agent learning. We show that the response graph is a simple and well-motivated model of strategic interaction which captures many non-trivial properties of a game, despite not depending on cardinal payoffs. We characterise the games which share a response graph with a zero-sum or potential game respectively, and demonstrate a duality between these sets. This allows us to understand the influence of these properties on the response graph. The response graphs of Matching Pennies and Coordination are shown to play a key role in all two-player games: every non-iteratively-dominated strategy takes part in a subgame with these graph structures. As a corollary, any game sharing a response graph with both a zero-sum game and potential game must be dominance-solvable. Finally, we demonstrate our results on some larger games., (© 2023. The Author(s).)