arXiv subjects

Mark Cannon

Publications and source records attributed to Mark Cannon.

At least 19 recordsLinked to original sources

arXiv2026

Robust Multi-step Model Predictive Control with Guaranteed Stability

We present a method of ensuring recursive feasibility and input-to-state stability of robust nonlinear Model Predictive Control (MPC) with multi-step predictors. Although feasibility guarantees are well-established for the case of single-step models applied recursively over a finite horizon, such guarantees are missing in naive MPC formulations that use distinct multi-step models to predict the system state at different future points in time. This issue arises because of potential inconsistencies in multi-step predictions generated at different times. Our approach performs an a priori sufficient feasibility check of the robust nonlinear MPC optimisation problem, and uses information from previous solutions to provide a fallback based on previously certified prediction sets. We illustrate the proposed predictor-substitution strategy with a simple numerical example.

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arXiv2026

Successive convex optimization for transformer encoder model predictive control

We propose a data-driven Model Predictive Control (MPC) framework that employs a transformer encoder to generate multi-step predictions. To handle the nonconvex attention mechanism, we derive difference of convex (DC) representations of the transformer encoder components and embed them in a successive convex programming (SCP) iteration. Recursive feasibility and convergence of the SCP iterates are guaranteed, and each iterate yields a solution estimate satisfying the problem constraints. Under mild assumptions, the SCP iteration converges to a locally optimal solution of the MPC problem. The approach is illustrated on a benchmark nonlinear control problem.

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arXiv2026

Robust adaptive NMPC using ellipsoidal tubes

We propose a computationally efficient nonlinear Model Predictive Control (NMPC) algorithm for safe, learning-based control. The system model is represented as an affine combination of basis functions with unknown parameters, and is subject to additive set-bounded disturbances. Our algorithm employs successive linearization around nominal predicted trajectories and accounts for uncertainties in predicted states due to linearization, model errors, and disturbances using ellipsoidal sets. The ellipsoidal tube-based approach ensures that constraints on control inputs and system states are satisfied. Robustness to uncertainty is ensured using bounds on linearization errors and a backtracking line search. We show that the ellipsoidal embedding of model uncertainty scales favourably with system dimensions in numerical simulations. The algorithm incorporates set membership parameter estimation, and provides guarantees of recursive feasibility and input-to-state practical stability.

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arXiv2026

Computationally Tractable Robust Nonlinear Model Predictive Control using DC Programming

We propose a computationally tractable, tube-based robust nonlinear model predictive control (MPC) framework using difference-of-convex (DC) functions and sequential convex programming. For systems with differentiable discrete time dynamics, we show how to construct systematic, data-driven DC model representations using polynomials and machine learning techniques. We develop a robust tube MPC scheme that convexifies the online optimization by linearizing the concave components of the model, and we provide guarantees of recursive feasibility and robust stability. We present three data-driven procedures for computing DC models and compare performance using a planar vertical take-off and landing (PVTOL) aircraft case study.

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arXiv2025

Learning-based Homothetic Tube MPC

In this paper, we study homothetic tube model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and mixed constraints on the state and input. Different from most existing work on robust MPC, we assume that the true disturbance set is unknown but a conservative surrogate is available a priori. Leveraging the real-time data, we develop an online learning algorithm to approximate the true disturbance set. This approximation and the corresponding constraints in the MPC optimisation are updated online using computationally convenient linear programs. We provide statistical gaps between the true and learned disturbance sets, based on which, probabilistic recursive feasibility of homothetic tube MPC problems is discussed. Numerical simulations are provided to demonstrate the efficacy of our proposed algorithm and compare with state-of-the-art MPC algorithms.

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arXiv2025

Deep Learning Model Predictive Control for Deep Brain Stimulation in Parkinson's Disease

We present a nonlinear data-driven Model Predictive Control (MPC) algorithm for deep brain stimulation (DBS) for the treatment of Parkinson's disease (PD). Although DBS is typically implemented in open-loop, closed-loop DBS (CLDBS) uses the amplitude of neural oscillations in specific frequency bands (e.g. beta 13-30 Hz) as a feedback signal, resulting in improved treatment outcomes with reduced side effects and slower rates of patient habituation to stimulation. To date, CLDBS has only been implemented in vivo with simple algorithms such as proportional, proportional-integral, and thresholded switching control. Our approach employs a multi-step predictor based on differences of input-convex neural networks to model the future evolution of beta oscillations. The use of a multi-step predictor enhances prediction accuracy over the optimization horizon and simplifies online computation. In tests using a simulated model of beta-band activity response and data from PD patients, we achieve reductions of more than 20% in both tracking error and control activity in comparison with existing CLDBS algorithms. The proposed control strategy provides a generalizable data-driven technique that can be applied to the treatment of PD and other diseases targeted by CLDBS, as well as to other neuromodulation techniques.

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arXiv2025

Deep learning adaptive Model Predictive Control of Fed-Batch Cultivations

Bioprocesses are often characterised by nonlinear and uncertain dynamics, posing particular challenges for model predictive control (MPC) algorithms due to their computational demands when applied to nonlinear systems. Recent advances in optimal control theory have demonstrated that concepts from convex optimisation, tube MPC, and differences of convex functions (DC) enable efficient, robust online process control. Our approach is based on DC decompositions of nonlinear dynamics and successive linearisations around predicted trajectories. By convexity, the linearisation errors have tight bounds and can be treated as bounded disturbances within a robust tube MPC framework. We describe a systematic, data-driven method for computing DC model representations using deep learning neural networks with a special convex structure, and explain how the resulting MPC optimisation can be solved using convex programming. For the problem of maximising product formation in a cultivation with uncertain model parameters, we design a controller that ensures robust constraint satisfaction and allows online estimation of unknown model parameters. Our results indicate that this method is a promising solution for computationally tractable, robust MPC of bioprocesses.

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arXiv2025

Safe adaptive NMPC using ellipsoidal tubes

A computationally efficient nonlinear Model Predictive Control (NMPC) algorithm is proposed for safe learning-based control with a system model represented by an incompletely known affine combination of basis functions and subject to additive set-bounded disturbances. The proposed algorithm employs successive linearization around predicted trajectories and accounts for the uncertain components of future states due to linearization, modelling errors and disturbances using ellipsoidal sets centered on the predicted nominal state trajectory. An ellipsoidal tube-based approach ensures satisfaction of constraints on control variables and model states. Feasibility is ensured using local bounds on linearization errors and a procedure based on a backtracking line search. We combine the approach with a set membership parameter estimation strategy in numerical simulations. We show that the ellipsoidal embedding of the predicted uncertainty scales favourably with the problem size. The resulting algorithm is recursively feasible and provides closed-loop stability and performance guarantees.

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arXiv2024

Robust targeted exploration for systems with non-stochastic disturbances

We propose a novel targeted exploration strategy designed specifically for uncertain linear time-invariant systems with energy-bounded disturbances, i.e., without any assumptions on the distribution of the disturbances. We use classical results characterising the set of non-falsified parameters consistent with energy-bounded disturbances. We derive a semidefinite program which computes an exploration strategy that guarantees a desired accuracy of the parameter estimate. This design is based on sufficient conditions on the spectral content of the exploration data that robustly account for initial parametric uncertainty. Finally, we highlight the applicability of the exploration strategy through a numerical example involving a nonlinear system.

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arXiv2023

Towards targeted exploration for non-stochastic disturbances

We present a novel targeted exploration strategy for linear time-invariant systems without stochastic assumptions on the noise, i.e., without requiring independence or zero mean, allowing for deterministic model misspecifications. This work utilizes classical data-dependent uncertainty bounds on the least-squares parameter estimates in the presence of energy-bounded noise. We provide a sufficient condition on the exploration data that ensures a desired error bound on the estimated parameter. Using common approximations, we derive a semidefinite program to compute the optimal sinusoidal input excitation. Finally, we highlight the differences and commonalities between the developed non-stochastic targeted exploration strategy and conventional exploration strategies based on classical identification bounds through a numerical example.

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arXiv2023

Data-driven robust MPC of tiltwing VTOL aircraft

This paper investigates robust tube-based Model Predictive Control (MPC) of a tiltwing Vertical Take-Off and Landing (VTOL) aircraft subject to wind disturbances and model uncertainty. Our approach is based on a Difference of Convex (DC) function decomposition of the dynamics to develop a computationally tractable optimisation with robust tubes for the system trajectories. We consider a case study of a VTOL aircraft subject to wind gusts and whose aerodynamics is defined from data.

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arXiv2023

Learning-based Rigid Tube Model Predictive Control

This paper is concerned with model predictive control (MPC) of discrete-time linear systems subject to bounded additive disturbance and mixed constraints on the state and input, whereas the true disturbance set is unknown. Unlike most existing work on robust MPC, we propose an algorithm incorporating online learning that builds on prior knowledge of the disturbance, i.e., a known but conservative disturbance set. We approximate the true disturbance set at each time step with a parameterised set, which is referred to as a quantified disturbance set, using disturbance realisations. A key novelty is that the parameterisation of these quantified disturbance sets enjoys desirable properties such that the quantified disturbance set and its corresponding rigid tube bounding disturbance propagation can be efficiently updated online. We provide statistical gaps between the true and quantified disturbance sets, based on which, probabilistic recursive feasibility of MPC optimisation problems is discussed. Numerical simulations are provided to demonstrate the effectiveness of our proposed algorithm and compare with conventional robust MPC algorithms.

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arXiv2023

A successive convexification approach for robust receding horizon control

A novel robust nonlinear model predictive control strategy is proposed for systems with nonlinear dynamics and convex state and control constraints. Using a sequential convex approximation approach and a difference of convex functions representation, the scheme constructs tubes that contain predicted model trajectories, accounting for approximation errors and disturbances, and guaranteeing constraint satisfaction. An optimal control problem is solved as a sequence of convex programs. We develop the scheme initially in the absence of external disturbances and show that the proposed nominal approach is non-conservative, with the solutions of successive convex programs converging to a locally optimal solution for the original optimal control problem. We extend the approach to the case of additive disturbances using a novel strategy for selecting linearization points. As a result we formulate a robust receding horizon strategy with guarantees of recursive feasibility closed-loop system stability.

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arXiv2023

Robust trajectory optimisation for transitions of tiltwing VTOL aircraft

We propose a method to generate robust and optimal trajectories for the transition of a tiltwing Vertical Take-Off and Landing (VTOL) aircraft leveraging concepts from convex optimisation, tube-based nonlinear Model Predictive Control (MPC) and Difference of Convex (DC) functions decomposition. The approach relies on computing DC decompositions of dynamic models in order to exploit convexity properties and develop a tractable robust optimisation that solves a sequence of convex programs converging to a local optimum of the trajectory generation problem. The algorithm developed is applied to an Urban Air Mobility case study. The resulting solutions are robust to approximation errors in dynamic models and provide safe trajectories for aggressive transition manoeuvres at constant altitude.

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arXiv2022

Adaptive robust predictive control with sample-based persistent excitation

We propose a robust adaptive Model Predictive Control (MPC) strategy with online set-based estimation for constrained linear systems with unknown parameters and bounded disturbances. A sample-based test applied to predicted trajectories is used to ensure convergence of parameter estimates by enforcing a persistence of excitation condition on the closed loop system. The control law robustly satisfies constraints and has guarantees of feasibility and input-to-state stability. Convergence of parameter set estimates to the actual system parameter vector is guaranteed under conditions on reachability and tightness of disturbance bounds.

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arXiv2022

Robust adaptive model predictive control with persistent excitation conditions

For constrained linear systems with bounded disturbances and parametric uncertainty, we propose a robust adaptive model predictive control strategy with online parameter estimation. Constraints enforcing persistently exciting closed loop control actions are introduced for a set-membership parameter identification scheme. The algorithm requires the online solution of a convex program, satisfies constraints robustly, and ensures recursive feasibility and input-to-state stability. Almost sure convergence to the actual system parameters is demonstrated under assumptions on stabilizability, reachability, and tight disturbance bounds.

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arXiv2022

Safeguarded Anderson acceleration for parametric nonexpansive operators

This paper describes the design of a safeguarding scheme for Anderson acceleration to improve its practical performance and stability when used for first-order optimisation methods. We show how the combination of a non-expansiveness condition, conditioning constraints, and memory restarts integrate well with solver algorithms that can be represented as fixed point operators with dynamically varying parameters. The performance of the scheme is demonstrated on seven different QP and SDP problem types, including more than 500 problems. The safeguarded Anderson acceleration scheme proposed in this paper is implemented in the open-source ADMM-based conic solver COSMO.

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arXiv2021

A Multirate Variational Approach to Nonlinear MPC

A multirate nonlinear model predictive control (NMPC) strategy is proposed for systems with dynamics and control inputs evolving on different timescales. The proposed multirate formulation of the system model and receding horizon optimal control problem allows larger time steps in the prediction horizon compared to single-rate schemes, providing computational savings while ensuring recursive feasibility. A multirate variational model is used with a tube-based successive linearization NMPC strategy. This allows either Jacobian linearization or linearization using quadratic and linear Taylor series approximations of the Lagrangian and generalized forces respectively, providing alternative means for computing linearization error bounds. The two approaches are shown to be equivalent for a specific choice of approximation points and their structure-preserving properties are investigated. Numerical examples are provided to illustrate the multirate approach, its conservation properties and computational savings.

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