arXiv subjects

Yuanbo Nie

Publications and source records attributed to Yuanbo Nie.

15 recordsLinked to original sources

arXiv2026

Feedback Linearisation with State Constraints

Feedback Linearisation (FBL) is a widely used technique that applies feedback laws to transform input-affine nonlinear control systems into linear control systems, allowing for the use of linear controller design methods such as pole placement. However, for problems with state constraints, controlling the linear system induced by FBL can be more challenging than controlling the original system. This is because simple state constraints in the original nonlinear system become complex nonlinear constraints in the FBL induced linearised system, thereby diminishing the advantages of linearisation. To avoid increasing the complexity of state constraints under FBL, this paper introduces a method to first augment system dynamics to capture state constraints before applying FBL. We show that our proposed augmentation method leads to ill-defined relative degrees at state constraint boundaries. However, we show that ill-defined relative degrees can be overcome by using a switching FBL controller. Numerical experiments illustrate the capabilities of this method for handling state constraints within the FBL framework.

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arXiv2025

NISE-PE Constraint: Data-Driven Predictive Control with Persistence of Excitation

Persistence of excitation (PE) is an important requirement for the successful operation of data-driven predictive control, as it ensures that the input-output data contains sufficient information about the underlying system dynamics. Nonetheless, this property is usually assumed rather than guaranteed. This paper introduces a novel data-driven predictive control formulation that maintains PE. The technical development that allows this is the characterisation of the nonexciting input set (NIS), i.e., the set of inputs that lead to loss of PE, and the consequent derivation of a pair of disjoint, linear inequality constraints on the input, termed NIS exclusion PE (NIS-PE) constraint, that, if satisfied, maintain PE. When used in a predictive control formulation, these constraints lead to a mixed-integer optimal control problem with a single binary variable or, equivalently, a pair of disjoint quadratic programming problems that can be efficiently and reliably solved. Numerical examples show how these constraints are able to maintain PE during the controller's operation, resulting in improved performance over conventional approaches for both time-invariant and time-varying systems.

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arXiv2025

Singular Arcs in Optimal Control: Closed-loop Implementations without Workarounds

Singular arcs emerge in the solutions of Optimal Control Problems (OCPs) when the optimal inputs on some finite time intervals cannot be directly obtained via the optimality conditions. Solving OCPs with singular arcs often requires tailored treatments, suitable for offline trajectory optimization. This approach can become increasingly impractical for online closed-loop implementations, especially for large-scale engineering problems. Recent development of Integrated Residual Methods (IRM) have indicated their suitability for handling singular arcs; the convergence of error measures in IRM automatically suppresses singular arc-induced fluctuations and leads to non-fluctuating solutions more suitable for practical problems. Through several examples, we demonstrate the advantages of solving OCPs with singular arcs using {IRM} under an economic model predictive control framework. In particular, the following observations are made: (i) IRM does not require special treatment for singular arcs, (ii) it solves the OCPs reliably with singular arc fluctuation suppressed, and (iii) the closed-loop results closely match the analytic optimal solutions.

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arXiv2025

Reliable Solution to Dynamic Optimization Problems using Integrated Residual Regularized Direct Collocation

Direct collocation is a widely used method for solving dynamic optimization problems (DOPs), but its implementation simplicity and computational efficiency are limited for challenging problems like those involving singular arcs. In this paper, we introduce the direct transcription method of integrated residual regularized direct collocation (IRR-DC). This method enforces dynamic constraints through a combination of explicit constraints and penalty terms within discretized DOPs. This method retains the implementation simplicity of direct collocation while significantly improving both solution accuracy and efficiency, particularly for challenging problem types. Through the examples, we demonstrate that for difficult problems where traditional direct collocation results in excessive fluctuations or large errors between collocation points, IRR-DC effectively suppresses oscillations and yields solutions with greater accuracy (several magnitudes lower in various error metrics) compared to other regularization alternatives.

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arXiv2024

Model Predictive Bang-Bang Controller Synthesis via Approximate Value Functions

In this paper, we propose a novel method for addressing Optimal Control Problems (OCPs) with input-affine dynamics and cost functions. This approach adopts a Model Predictive Control (MPC) strategy, wherein a controller is synthesized to handle an approximated OCP within a finite time horizon. Upon reaching this horizon, the controller is re-calibrated to tackle another approximation of the OCP, with the approximation updated based on the final state and time information. To tackle each OCP instance, all non-polynomial terms are Taylor-expanded about the current time and state and the resulting Hamilton-Jacobi-Bellman (HJB) PDE is solved via Sum-of-Squares (SOS) programming, providing us with an approximate polynomial value function that can be used to synthesize a bang-bang controller.

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arXiv2024

Tracking-in-range Formulations for Numerical Optimal Control

In contrast to set-point tracking which aims to reduce the tracking error between the tracker and the reference, tracking-in-range problems only focus on whether the tracker is within a given range around the reference, making it more suitable for the mission specifications of many practical applications. In this work, we present novel optimal control formulations to solve tracking-in-range problems, for both problems requiring the tracker to be always in range, and problems allowing the tracker to go out of range to yield overall better outcomes. As the problem naturally involves discontinuous functions, we present alternative formulations and regularisation strategies to improve the performance of numerical solvers. The extension to in-range tracking with multiple trackers and in-range tracking in high dimensional space are also discussed and illustrated with numerical examples, demonstrating substantial increases in mission duration in comparison to traditional set-point tracking.

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arXiv2022

Solving optimal control problems with non-smooth solutions using an integrated residual method and flexible mesh

Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical methods assume state and input trajectories are continuous and differentiable or smooth, our method is able to capture discontinuities in the solution by introducing time-mesh nodes as decision variables. This allows one to obtain a higher accuracy solution for the same number of mesh nodes compared to a fixed time-mesh approach. Furthermore, we propose to first solve a sequence of suitably-defined least-squares problems to ensure that the error in the dynamic equation is below a given tolerance. The cost functional is then minimized subject to an inequality constraint on the dynamic equation residual. We demonstrate our implementation on an optimal control problem that has a chattering solution. Solving such a problem is difficult, since the solution involves infinitely many switches of decreasing duration. This simulation shows how the flexible mesh is able to capture discontinuities present in the solution and achieve superlinear convergence as the number of mesh intervals is increased.

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arXiv2022

Fast and accurate method for computing non-smooth solutions to constrained control problems

Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems with constraints. State-of-the-art methods use fixed mesh schemes, which cannot achieve superlinear convergence in the presence of non-smooth solutions. In this paper, we propose using a flexible mesh in an integrated residual method. The locations of the mesh nodes are introduced as decision variables, and constraints are added to set upper and lower bounds on the size of the mesh intervals. We compare our approach to a uniform fixed mesh on a real-world satellite reorientation example. This example demonstrates that the flexible mesh enables the solver to automatically locate the discontinuities in the solution, has superlinear convergence and faster solve times, while achieving the same accuracy as a fixed mesh.

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arXiv2022

Solving Dynamic Optimization Problems to a Specified Accuracy: An Alternating Approach using Integrated Residuals

We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct collocation, the new approach alternates between minimizing and constraining the squared norm of the dynamic constraint residuals integrated along the whole solution trajectories. As a result, the method can 1) obtain solutions of higher accuracy for the same mesh compared to direct collocation methods, 2) enables a flexible trade-off between solution accuracy and optimality, 3) provides reliable solutions for challenging problems, including those with singular arcs and high-index differential algebraic equations.

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arXiv2021

Towards a Framework for Nonlinear Predictive Control using Derivative-Free Optimization

The use of derivative-based solvers to compute solutions to optimal control problems with non-differentiable cost or dynamics often requires reformulations or relaxations that complicate the implementation or increase computational complexity. We present an initial framework for using the derivative-free Mesh Adaptive Direct Search (MADS) algorithm to solve Nonlinear Model Predictive Control problems with non-differentiable features without the need for reformulation. The MADS algorithm performs a structured search of the input space by simulating selected system trajectories and computing the subsequent cost value. We propose handling the path constraints and the Lagrange cost term by augmenting the system dynamics with additional states to compute the violation and cost value alongside the state trajectories, eliminating the need for reconstructing the state trajectories in a separate phase. We demonstrate the practicality of this framework by solving a robust rocket control problem, where the objective is to reach a target altitude as close as possible, given a system with uncertain parameters. This example uses a non-differentiable cost function and simulates two different system trajectories simultaneously, with each system having its own free final time.

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arXiv2020

Direct Transcription for Dynamic Optimization: A Tutorial with a Case Study on Dual-Patient Ventilation During the COVID-19 Pandemic

A variety of optimal control, estimation, system identification and design problems can be formulated as functional optimization problems with differential equality and inequality constraints. Since these problems are infinite-dimensional and often do not have a known analytical solution, one has to resort to numerical methods to compute an approximate solution. This paper uses a unifying notation to outline some of the techniques used in the transcription step of simultaneous direct methods (which discretize-then-optimize) for solving continuous-time dynamic optimization problems. We focus on collocation, integrated residual and Runge-Kutta schemes. These transcription methods are then applied to a simulation case study to answer a question that arose during the COVID-19 pandemic, namely: If there are not enough ventilators, is it possible to ventilate more than one patient on a single ventilator? The results suggest that it is possible, in principle, to estimate individual patient parameters sufficiently accurately, using a relatively small number of flow rate measurements, without needing to disconnect a patient from the system or needing more than one flow rate sensor. We also show that it is possible to ensure that two different patients can indeed receive their desired tidal volume, by modifying the resistance experienced by the air flow to each patient and controlling the ventilator pressure.

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arXiv2020

Efficient Implementation of Rate Constraints for Nonlinear Optimal Control

We propose a general approach to directly implement rate constraints on the discretization mesh for all collocation methods, for both state and input variables. Unlike conventional approaches that may lead to singular control arcs, the solution of this on-mesh implementation has better properties. Moreover, computational speedups of more than 30% can be achieved by exploiting the properties of the resulting linear constraint equations.

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arXiv2019

Joint Optimization of Transmission and Propulsion in UAV-Assisted Communication Networks

The communication energy in a wireless network of mobile autonomous agents should be defined to include the propulsion energy as well as the transmission energy used to facilitate information transfer. We therefore develop communicationtheoretic and Newtonian dynamic models of the communication and locomotion expenditures of an unmanned aerial vehicle (UAV). These models are used to formulate a novel nonlinear optimal control problem (OCP) for arbitrary networks of autonomous agents. This is the first work to consider mobility as a decision variable in UAV networks with multiple access channels. Where possible, we compare our results with known analytic solutions for particular single-hop network configurations. The OCP is then applied to a multiple-node UAV network for which previous results cannot be readily extended. Numerical results demonstrate increased network capacity and communication energy savings upwards of 70% when compared to more naive communication policies.

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arXiv2019

External Constraint Handling for Solving Optimal Control Problems with Simultaneous Approaches and Interior Point Methods

Inactive constraints do not contribute to the solution of an optimal control problem, but increase the problem size and burden the numerical computations. We present a novel strategy for handling inactive constraints efficiently by systematically removing the inactive and redundant constraints. The method is designed to be used together with simultaneous approaches under a mesh refinement framework, with mild assumptions that the original problem has feasible solutions, and the initial solve of the problem is successful. The method is tailored for interior point-based solvers, which are known to be very sensitive to the choice of initial points in terms of feasibility. In the example problem shown, the proposed scheme achieves more than a 40% reduction in computation time.

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arXiv2019

Efficient and More Accurate Representation of Solution Trajectories in Numerical Optimal Control

We show via examples that, when solving optimal control problems, representing the optimal state and input trajectory directly using interpolation schemes may not be the best choice. Due to the lack of considerations for solution trajectories in-between collocation points, large errors may occur, posing risks if this solution is to be applied. A novel solution representation method is proposed, capable of yielding a solution of much higher accuracy for the same discretization mesh. This is achieved by minimizing the integral of the residual error for the overall trajectory, instead of forcing the errors to be zero only at collocation points. In this way, the requirement for mesh resolution can be significantly reduced, leaving the problem dimensions relatively small. This particular formulation also avoids some of the drawbacks found in the earlier work of integrated residual minimization, leading to more efficient computations.

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