arXiv subjects

Mark Cannon

Publications and source records attributed to Mark Cannon.

At least 37 records · Page 2Linked to original sources

arXiv2022

Predictive energy management for hybrid electric aircraft propulsion systems

We present a Model Predictive Control (MPC) algorithm for energy management in aircraft with hybrid electric propulsion systems consisting of gas turbine and electric motor components. Series and parallel configurations are considered. By combining a point-mass aircraft dynamical model with models of electrical losses and losses in the gas turbine, the fuel consumed over a given future flight path is minimised subject to constraints on the battery, electric motor and gas turbine. The optimization is formulated as a convex problem under mild assumptions and its solution is used to define a predictive energy management control law that takes into account the variation in aircraft mass during flight. We investigate the performance of algorithms for solving this problem. An Alternating Direction Method of Multipliers (ADMM) algorithm is proposed and compared with a general purpose convex interior point solver. We also show that the ADMM implementation reduces the required computation time by orders of magnitude in comparison with a general purpose nonlinear programming solver, making it suitable for real-time supervisory energy management control.

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arXiv2022

Scenario Model Predictive Control for Data-based Energy Management in Plug-in Hybrid Electric Vehicles

One of the major limitations of optimization-based strategies for allocating the power flow in hybrid powertrains is that they rely on predictions of future power demand. These predictions are inherently uncertain as they are dependent on complex human behaviours that are challenging to model accurately. This paper proposes a data-based scenario model predictive control framework, where the inputs are determined at each control update by optimizing the power allocation over multiple previous examples of a route being driven. The proposed energy management optimization is convex, and results from scenario optimization are used to bound the confidence that the one-step-ahead optimization will be feasible with given probability. It is shown through numerical simulation that scenario model predictive control (MPC) obtains the same reduction in fuel consumption as nominal MPC with full preview of future driver behaviour, and that the scenario MPC optimization can be solved efficiently using a tailored optimization algorithm.

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arXiv2022

Stochastic output feedback MPC with intermittent observations

This paper designs a model predictive control (MPC) law for constrained linear systems with stochastic additive disturbances and noisy measurements, minimising a discounted cost subject to a discounted expectation constraint. It is assumed that sensor data is lost with a known probability. Taking into account the data losses modelled by a Bernoulli process, we parameterise the predicted control policy as an affine function of future observations and obtain a convex linear-quadratic optimal control problem. Constraint satisfaction and a discounted cost bound are ensured without imposing bounds on the distributions of the disturbance and noise inputs. In addition, the average long-run undiscounted closed loop cost is shown to be finite if the discount factor takes appropriate values. We analyse robustness of the proposed control law with respect to possible uncertainties in the arrival probability of sensor data and we bound the impact of these uncertainties on constraint satisfaction and the discounted cost. Numerical simulations are provided to illustrate these results.

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arXiv2021

Fast optimal trajectory generation for a tiltwing VTOL aircraft with application to urban air mobility

We solve the minimum-thrust optimal trajectory generation problem for the transition of a tiltwing Vertical Take-Off and Landing (VTOL) aircraft using convex optimisation. The method is based on a change of differential operator that allows us to express the simplified point-mass dynamics along a prescribed path and formulate the original nonlinear problem in terms of a pair of convex programs. A case study involving the Airbus A3 Vahana VTOL aircraft is considered for forward and backward transitions. The presented approach provides a fast method to generate a safe optimal transition for a tiltwing VTOL aircraft that can further be leveraged online for control, and guidance purposes.

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arXiv2021

Stochastic MPC with Dynamic Feedback Gain Selection and Discounted Probabilistic Constraints

This paper considers linear discrete-time systems with additive disturbances, and designs a Model Predictive Control (MPC) law incorporating a dynamic feedback gain to minimise a quadratic cost function subject to a single chance constraint. The feedback gain is selected online and we provide two selection methods based on minimising upper bounds on predicted costs. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalising violation probabilities close to the initial time and assigning violation probabilities in the far future with vanishingly small weights, this form of constraints allows for an MPC law with guarantees of recursive feasibility without a boundedness assumption on the disturbance. A computationally convenient MPC optimisation problem is formulated using Chebyshev's inequality and we introduce an online constraint-tightening technique to ensure recursive feasibility. The closed loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition. With dynamic feedback gain selection, the closed loop cost is reduced and conservativeness of Chebyshev's inequality is mitigated. Also, a larger feasible set of initial conditions can be obtained. Numerical simulations are given to show these results.

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arXiv2020

A multirate variational approach to simulation and optimal control for flexible spacecraft

We propose an optimal control method for simultaneous slewing and vibration control of flexible spacecraft. Considering dynamics on different time scales, the optimal control problem is discretized on micro and macro time grids using a multirate variational approach. The description of the system and the necessary optimality conditions are derived through the discrete Lagrange-d'Alembert principle. The discrete problem retains the conservation properties of the continuous model and achieves high fidelity simulation at a reduced computational cost. Simulation results for a single-axis rotational maneuver demonstrate vibration suppression and achieve the same accuracy as the single rate method at reduced computational cost.

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arXiv2020

Optimal Power Allocation in Battery/Supercapacitor Electric Vehicles using Convex Optimization

This paper presents a framework for optimizing the power allocation between a battery and supercapacitor in an electric vehicle energy storage system. A convex optimal control formulation is proposed that minimizes total energy consumption whilst enforcing hard constraints on power output and total energy stored in the battery and supercapacitor. An alternating direction method of multipliers (ADMM) algorithm is proposed, for which the computational and memory requirements scale linearly with the length of the prediction horizon (and can be reduced using parallel processing). The optimal controller is compared with a low-pass filter against an all-battery baseline in numerical simulations, where it is shown to provide significant improvement in battery degradation (inferred through reductions of 71.4% in peak battery power, 21.0% in root-mean-squared battery power, and 13.7% in battery throughput), and a reduction of 5.7% in energy consumption. It is also shown that the ADMM algorithm can solve the optimization problem in a fraction of a second for prediction horizons of more than 15 minutes, and is therefore a promising candidate for online receding-horizon control.

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arXiv2020

COSMO: A conic operator splitting method for convex conic problems

This paper describes the Conic Operator Splitting Method (COSMO) solver, an operator splitting algorithm for convex optimisation problems with quadratic objective function and conic constraints. At each step the algorithm alternates between solving a quasi-definite linear system with a constant coefficient matrix and a projection onto convex sets. The low per-iteration computational cost makes the method particularly efficient for large problems, e.g. semidefinite programs that arise in portfolio optimisation, graph theory, and robust control. Moreover, the solver uses chordal decomposition techniques and a new clique merging algorithm to effectively exploit sparsity in large, structured semidefinite programs. A number of benchmarks against other state-of-the-art solvers for a variety of problems show the effectiveness of our approach. Our Julia implementation is open-source, designed to be extended and customised by the user, and is integrated into the Julia optimisation ecosystem.

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arXiv2020

Robust Adaptive Model Predictive Control: Performance and Parameter Estimation

For systems with uncertain linear models, bounded additive disturbances and state and control constraints, a robust model predictive control algorithm incorporating online model adaptation is proposed. Sets of model parameters are identified online and employed in a robust tube MPC strategy with a nominal cost. The algorithm is shown to be recursively feasible and input-to-state stable. Computational tractability is ensured by using polytopic sets of fixed complexity to bound parameter sets and predicted states. Convex conditions for persistence of excitation are derived and are related to probabilistic rates of convergence and asymptotic bounds on parameter set estimates. We discuss how to balance conflicting requirements on control signals for achieving good tracking performance and parameter set estimate accuracy. Conditions for convergence of the estimated parameter set are discussed for the case of fixed complexity parameter set estimates, inexact disturbance bounds and noisy measurements.

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arXiv2020

A clique graph based merging strategy for decomposable SDPs

Chordal decomposition techniques are used to reduce large structured positive semidefinite matrix constraints in semidefinite programs (SDPs). The resulting equivalent problem contains multiple smaller constraints on the nonzero blocks (or cliques) of the original problem matrices. This usually leads to a significant reduction in the overall solve time. A further reduction is possible by remerging cliques with significant overlap. The degree of overlap for which this is effective is dependent on the particular solution algorithm and hardware to be employed. We propose a novel clique merging approach that utilizes the clique graph to identify suitable merge candidates. We show its performance by comparing it with two existing methods on selected problems from a benchmark library. Our approach is implemented in the latest version of the conic ADMM-solver COSMO.

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arXiv2020

Output feedback stochastic MPC with packet losses

The paper considers constrained linear systems with stochastic additive disturbances and noisy measurements transmitted over a lossy communication channel. We propose a model predictive control (MPC) law that minimizes a discounted cost subject to a discounted expectation constraint. Sensor data is assumed to be lost with known probability, and data losses are accounted for by expressing the predicted control policy as an affine function of future observations, which results in a convex optimal control problem. An online constraint-tightening technique ensures recursive feasibility of the online optimization and satisfaction of the expectation constraint without bounds on the distributions of the noise and disturbance inputs. The cost evaluated along trajectories of the closed loop system is shown to be bounded by the optimal predicted cost. A numerical example is given to illustrate these results.

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arXiv2020

Optimal energy management for hybrid electric aircraft

A convex formulation is proposed for optimal energy management in aircraft with hybrid propulsion systems consisting of gas turbine and electric motor components. By combining a point-mass aircraft dynamical model with models of electrical and mechanical powertrain losses, the fuel consumed over a planned future flight path is minimised subject to constraints on the battery, electric motor and gas turbine. The resulting optimisation problem is used to define a predictive energy management control law that takes into account the variation in aircraft mass during flight. A simulation study based on a representative 100-seat aircraft with a prototype parallel hybrid electric propulsion system is used to investigate the properties of the controller. We show that an optimisation-based control strategy can provide significant fuel savings over heuristic energy management strategies in this context.

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arXiv2020

Convergence of stochastic nonlinear systems and implications for Stochastic Model Predictive Control

The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that ensure closed-loop performance bounds and boundedness of the state, but tight ultimate bounds for the state and non-conservative performance bounds are typically not determined. In this work we use an input-to-state stability property to find conditions that imply convergence with probability 1 of a disturbed nonlinear system to a minimal robust positively invariant set. We discuss implications for the convergence of the state and control laws of stochastic MPC formulations, and we prove convergence results for several existing stochastic MPC formulations for linear and nonlinear systems.

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arXiv2020

Infinite-Horizon Differentiable Model Predictive Control

This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic Riccati equation (DARE), so that the learned controller can be proven to be stabilizing in closed-loop. A central contribution is the derivation of the analytical derivative of the solution of the DARE, thereby allowing the use of differentiation-based learning methods. A further contribution is the structure of the MPC optimization problem: an augmented Lagrangian method ensures that the MPC optimization is feasible throughout training whilst enforcing hard constraints on state and input, and a pre-stabilizing controller ensures that the MPC solution and derivatives are accurate at each iteration. The learning capabilities of the framework are demonstrated in a set of numerical studies.

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arXiv2019

Energy Management in Plug-in Hybrid Electric Vehicles: Convex Optimization Algorithms for Model Predictive Control

This paper details an investigation into the computational performance of algorithms used for solving a convex formulation of the optimization problem associated with model predictive control for energy management in hybrid electric vehicles with nonlinear losses. A projected interior point method is proposed, where the size and complexity of the Newton step matrix inversion is reduced by applying inequality constraints on the control input as a projection, and its properties are demonstrated through simulation in comparison with an alternating direction method of multipliers (ADMM) algorithm, and general purpose convex optimization software CVX. It is found that the ADMM algorithm has favourable properties when a solution with modest accuracy is required, whereas the projected interior point method is favourable when high accuracy is required, and that both are significantly faster than CVX.

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arXiv2019

Parallel ADMM for robust quadratic optimal resource allocation problems

An alternating direction method of multipliers (ADMM) solver is described for optimal resource allocation problems with separable convex quadratic costs and constraints and linear coupling constraints. We describe a parallel implementation of the solver on a graphics processing unit (GPU) using a bespoke quartic function minimizer. An application to robust optimal energy management in hybrid electric vehicles is described, and the results of numerical simulations comparing the computation times of the parallel GPU implementation with those of an equivalent serial implementation are presented.

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arXiv2019

Fast Optimal Energy Management with Engine On/Off Decisions for Plug-in Hybrid Electric Vehicles

In this paper we demonstrate a novel alternating direction method of multipliers (ADMM) algorithm for the solution of the hybrid vehicle energy management problem considering both power split and engine on/off decisions. The solution of a convex relaxation of the problem is used to initialize the optimization, which is necessarily nonconvex, and whilst only local convergence can be guaranteed, it is demonstrated that the algorithm will terminate with the optimal power split for the given engine switching sequence. The algorithm is compared in simulation against a charge-depleting/charge-sustaining (CDCS) strategy and dynamic programming (DP) using real world driver behaviour data, and it is demonstrated that the algorithm achieves 90\% of the fuel savings obtained using DP with a 3000-fold reduction in computational time.

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arXiv2019

On the convergence of stochastic MPC to terminal modes of operation

The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of the state, but convergence to a terminal control law is typically not shown. In this work we use results on general state space Markov chains to find conditions that guarantee convergence of disturbed nonlinear systems to terminal modes of operation, so that they converge in probability to a priori known terminal linear feedback laws and achieve time-average performance equal to that of the terminal control law. We discuss implications for the convergence of control laws in stochastic MPC formulations, in particular we prove convergence for two formulations of stochastic MPC.

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