Search Results (27)

In this paper, we propose a convexification method for the reversed-time problem of a complex Ginzburg–Landau equation by introducing a new Carleman estimate for the complex Ginzburg–Landau operator, which holds on an arbitrary time interval. We construct a weighted Tikhonov-like functional and prove its global strict convexity. We establish both the existence and uniqueness of the minimizer, along with the global convergence of the associated gradient projection method toward the exact solution. These results ensure global convergence, unlike conventional least-squares minimization techniques, which only offer local convergence. Full article

Autonomous drifting requires coordinated steering and driving actuation near the tire friction limit, where strong tire nonlinearity and rapidly changing constraints challenge control accuracy and real-time solvability. This article proposes an equilibrium-free successive convexification (SCvx) nonlinear model predictive control framework for drift tracking under constant and varying curvature conditions. The front steering angle and rear-axle longitudinal force are optimized jointly subject to actuator, state, and tire-force constraints. A physics-guided MLP residual tire model is introduced to improve rear-tire-force prediction. Online reference generation determines the heading error, yaw rate, and rear longitudinal force targets from path curvature, lateral error, sideslip variation, and rear slip ratio error, eliminating the need for precomputed drift equilibria. SCvx converts the nonlinear predictive control problem into convex subproblems using virtual control, slack variables, and trust regions. Hardware-in-the-loop experiments confirm stable actuator coordination under both test conditions. Under varying curvature drifting, the proposed method reduces lateral error, velocity error, and yaw rate error by 39.2%, 53.7%, and 24.9%, respectively, compared with the Fiala tire model using the same solver. The results demonstrate improved tracking accuracy and numerical robustness for constrained autonomous drift control. Full article

This overview paper highlights the idea that the polytopic approach is more than a modeling technique. It proposes a unified perspective in which polytopic representations constitute a conceptual bridge between complex system dynamics and convex analysis. From modeling to control, the polytope is not only limited to a geometric interpretation but is used as a methodological principle—an intelligent sensor system for structuring uncertainty, representing a nonlinear behaviors, and enabling decision-making, even for critical safety systems. Indeed, the polytopic approach should not be viewed merely as a convexification tool, but as a way of thinking about complexity, i.e., a structured methodology linking representation, uncertainty management, and control synthesis. For this purpose, this work focuses on safety-critical systems, i.e., cyber-physical systems operating under malicious cyber-attacks, where ensuring resilience has become a major challenge. The review highlights recent developments that extend classical polytopic approaches beyond robust control and toward cyber-resilient estimation and control, including false-data injection attack modeling, simultaneous state and attack estimation, resilient observer-based control, and event-triggered control under communication constraints. The paper also discusses how these developments position the polytopic framework with respect to recent advances in cyber-physical security and resilient control. Overall, the proposed perspective illustrates how polytopic representations have evolved into a unifying paradigm for addressing nonlinear dynamics, cyber-attacks, uncertainties, and network-induced constraints while enhancing the resilience, reliability, and operational safety of safety-critical cyber-physical systems. Full article

Unmanned aerial vehicles (UAVs) are increasingly expected to support both wireless communication and logistics missions, creating a need for integrated operation strategies that jointly manage data collection and physical item handling. This paper investigates a UAV system that simultaneously performs uplink communication with multiple ground nodes (GNs) while completing time-constrained item-pickup tasks. To enhance both throughput and fairness across GNs, we maximize the proportional fair spectral efficiency of GNs while ensuring that all items are collected within the required mission duration under payload and geographical constraints. The resulting formulation constitutes a mixed-integer nonconvex optimization problem involving binary pickup assignments, binary communication scheduling, and trajectory-dependent channel coupling, making direct global optimization intractable. To address this challenge, we develop an iterative convexification framework that integrates the successive convex approximation and the penalty convex–concave procedure within a block coordinate descent structure, enabling efficient joint optimization of trajectory, pickup timing/sequence, and GN scheduling. Simulation results validate that the proposed scheme dynamically shapes the UAV trajectory to improve channel conditions without violating the pickup deadline and compensates disadvantaged GNs through proportional fair scheduling. As a result, it consistently outperforms the baseline strategies under various system parameters. Full article

With the development of rocket technology, achieving high-precision landing has become a key technical challenge in the field of aerospace. To cope with this challenge, we propose a lossless convexification algorithm based on the integral pseudospectral method in this paper. Firstly, for the fuel optimization problem, the continuous dynamic equations and constraints are discretized with high accuracy using an integral-type pseudospectral method. By constructing a global integration matrix at Legendre–Gauss nodes, the original complex continuous problem is effectively transformed into a discrete form that is more tractable for numerical optimization. Secondly, the non-convex constraints are transformed using the lossless convexification technique, thereby reformulating the original problem as a second-order cone programming (SOCP) problem. The effectiveness of the proposed algorithm is validated through numerical simulations, which demonstrate high landing accuracy, robustness, and fuel efficiency. These results highlight the algorithm’s high performance and strong potential for practical application in space missions. Full article

This paper addresses the critical multiple-uncertainty challenge in laser link acquisition for space gravitational wave detection missions—a key bottleneck where spacecraft attitude alignment for laser link establishment is perturbed by inherent random disturbances in such missions, while also needing to balance ultra-high attitude precision, fuel efficiency, and compliance with engineering constraints. To tackle this, a convex optimization-based attitude control strategy integrating covariance control and free terminal time optimization is proposed. Specifically, a stochastic attitude dynamics model is first established to explicitly incorporate the aforementioned random disturbances. Subsequently, an objective function is designed to simultaneously minimize terminal state error and fuel consumption, with three key constraints (covariance constraints, pointing constraints, and torque saturation constraints) integrated into the convex optimization framework. Furthermore, to resolve non-convex terms in chance constraints, this study employs a hierarchical convexification method that combines Schur’s complementary theorem, second-order cone relaxation, and Taylor expansion techniques. This approach ensures lossless relaxation, renders the optimization problem computationally tractable without sacrificing solution accuracy, and overcomes the shortcomings of traditional convexification methods in handling chance constraints. Finally, numerical simulations demonstrate that the proposed method adheres to engineering constraints while maintaining spacecraft attitude errors below 1 μrad under environmental uncertainties. This study provides a convex optimization solution for laser link acquisition in space gravitational wave detection missions considering uncertainty conditions, and its framework can be extended to the optimal design of other stochastically uncertain systems. Full article

The reconfiguration of distribution networks plays a crucial role in minimizing active power losses and enhancing reliability, but the problem becomes increasingly complex with the integration of distributed generation (DG). Traditional optimization methods and even earlier hybrid metaheuristics often suffer from premature convergence or require problem reformulations that compromise feasibility. To overcome these limitations, this paper proposes a novel hybrid algorithm that couples Particle Swarm Optimization (PSO) with Simulated Annealing (SA) through an adaptive inertia weight mechanism derived from the Lundy–Mees cooling schedule. Unlike prior hybrid approaches, our method directly addresses the original non-convex, combinatorial nature of the Distribution Network Reconfiguration (DNR) problem without convexification or post-processing adjustments. The main contributions of this study are fourfold: (i) proposing a PSO-SA hybridization strategy that enhances global exploration and avoids stagnation; (ii) introducing an adaptive inertia weight rule tuned by SA, more effective than traditional schemes; (iii) applying a stagnation-based stopping criterion to speed up convergence and reduce computational cost; and (iv) validating the approach on 5-, 33-, and 69-bus systems, with and without DG, showing robustness, recurrence rates above 80%, and low variability compared to conventional PSO. Simulation results confirm that the proposed PSO-SA algorithm achieves superior performance in both loss minimization and solution stability, positioning it as a competitive and scalable alternative for modern active distribution systems. Full article

This paper investigates the design of optimal low-thrust transfers between relative planar and spatial quasi-satellite orbits (QSOs) in the Earth–Moon system under the Circular Restricted Three-Body Problem (CR3BP). A key contribution is the adaptation of a trajectory optimization framework, previously applied to halo orbit transfers, to accommodate the unique challenges of QSO families, especially the transition between planar and spatial configurations. The method employs a refined beam search strategy to construct diverse initial guess chains, which are then optimized via a successive convexification algorithm tailored for the spatial dynamics of QSOs. Additionally, a linear–quadratic regulator (LQR)-based control scheme is implemented to ensure long-term station-keeping of the final 3D-QSO. Simulation results demonstrate the feasibility of connecting planar and spatial QSOs with minimum-fuel trajectories while maintaining bounded terminal deviations, offering new tools for future Earth–Moon logistics and navigation infrastructure. Key findings include the successful design of low-thrust transfer trajectories between planar QSOs and 1:5 3D-QSOs, with a minimum total $\mathsf{\Delta }V$ of 195.576 m/s over a time of flight (ToF) of 261 days, and a minimum ToF of 41 days with a total $\mathsf{\Delta }V$ of 270.507 m/s. Additionally, the application of LQR control demonstrated the ability to maintain 1:5 3D-QSO families around the Moon with less than 12 mm/s $\mathsf{\Delta }V$ over two months. This research provides valuable insights into the optimization of low-thrust transfer trajectories and the application of advanced control techniques for space missions, particularly those targeting lunar and planetary satellite exploration. Full article

This paper proposes a robot trajectory planning method focused on time and jerk optimization under compound constraints. First, the robot path-tracking task is parameterized by incorporating both kinematic and dynamic constraints in joint and Cartesian spaces, establishing a time-optimal trajectory optimization model. To achieve C³ continuity in joint motion, joint-motion continuity conditions are analyzed, and optimization variables are reconstructed using piecewise cubic splines with corresponding continuity constraints. Considering the nonlinear and nonconvex characteristics of jerk constraints, the time-optimal planning model is decomposed into two second-order cone programming (SOCP) subproblems, achieving linear convexification of the original problem. Additionally, the objective function is improved to optimize both time and joint jerk simultaneously. Experimental results confirm that the proposed method effectively improves robot efficiency and trajectory smoothness. Full article

This article investigates robust optimality conditions and duality results for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (UNMPVC). Mathematical programming problems with vanishing constraints constitute a distinctive class of constrained optimization problems because of the presence of complementarity constraints. Moreover, uncertainties are inherent in various real-life problems. The aim of this article is to identify an optimal solution to an uncertain optimization problem with vanishing constraints that remains feasible in every possible future scenario. Stationary conditions are necessary conditions for optimality in mathematical programming problems with vanishing constraints. These conditions can be derived under various constraint qualifications. Employing the properties of convexificators, we introduce generalized standard Abadie constraint qualification (GS-ACQ) for the considered problem, UNMPVC. We introduce a generalized robust version of nonsmooth stationary conditions, namely a weakly stationary point, a Mordukhovich stationary point, and a strong stationary point (RS-stationary) for UNMPVC. By employing GS-ACQ, we establish the necessary conditions for a local weak Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we derive sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type and Mond–Weir-type robust dual models corresponding to the primal problem, UNMPVC. Full article

In this article, we investigate a class of non-smooth semidefinite multiobjective programming problems with inequality and equality constraints (in short, NSMPP). We establish the convex separation theorem for the space of symmetric matrices. Employing the properties of the convexificators, we establish Fritz John (in short, FJ)-type necessary optimality conditions for NSMPP. Subsequently, we introduce a generalized version of Abadie constraint qualification (in short, NSMPP-ACQ) for the considered problem, NSMPP. Employing NSMPP-ACQ, we establish strong Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions for NSMPP. Moreover, we establish sufficient optimality conditions for NSMPP under generalized convexity assumptions. In addition to this, we introduce the generalized versions of various other constraint qualifications, namely Kuhn-Tucker constraint qualification (in short, NSMPP-KTCQ), Zangwill constraint qualification (in short, NSMPP-ZCQ), basic constraint qualification (in short, NSMPP-BCQ), and Mangasarian-Fromovitz constraint qualification (in short, NSMPP-MFCQ), for the considered problem NSMPP and derive the interrelationships among them. Several illustrative examples are furnished to demonstrate the significance of the established results. Full article

Due to the strong nonlinearity in the reentry trajectory planning problem for reusable launch vehicles (RLVs), the scale of the problem after high-precision discretization can become significantly large, and the non-convex path constraints are prone to exceed limits. Meanwhile, the objective function oscillation phenomenon may occur due to successive convexification, which results in poor convergence. To address these issues, a novel sequential convex programming (SCP) method utilizing modified hp-adaptive mesh refinement and variable quadratic penalty is proposed in this paper. Firstly, a local mesh refinement algorithm based on constraint violation is proposed. Additional mesh intervals and mesh points are added in the vicinity of the constraint violation points, which improves the satisfaction of non-convex path constraints. Secondly, a sliding window-based mesh reduction algorithm is designed and introduced into the hp-adaptive pseudospectral (PS) method. Unnecessary mesh intervals are merged to reduce the scale of the problem. Thirdly, a variable quadratic penalty-based SCP method is proposed. The quadratic penalty term related to the iteration direction and the weight coefficient updating strategy is designed to eliminate the oscillation. Numerical simulation results show that the proposed method can strictly satisfy path constraints while the computational efficiency and convergence of SCP are improved. Full article

This article deals with mathematical programs with vanishing constraints (MPVCs) involving lower semi-continuous functions. We introduce generalized Abadie constraint qualification (ACQ) and MPVC-ACQ in terms of directional convexificators and derive necessary KKT-type optimality conditions. We also derive sufficient conditions for global optimality for the MPVC under convexity utilizing directional convexificators. Further, we introduce a Wolfe-type dual model in terms of directional convexificators and derive duality results. The results are well illustrated by examples. Full article

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm. Full article

This paper presents a fast trajectory optimization method combining the hp-Legendre pseudospectral method and convex optimization for the 6-Degree-of-Freedom rocket-powered landing problem. To accelerate calculations, this paper combines the Legendre pseudospectral method with a linearization method for convexification, and an hp method that can divide the mesh is introduced to reduce the computational workload. In terms of accuracy, a trust region update strategy that can control the solution process is presented to approximate the original problem iteratively. Convergence analysis is provided as evidence, substantiating that any solution produced by the hp-Legendre pseudospectral convex method is not only feasible but potentially optimal for the original problem. The effectiveness of the proposed method is demonstrated by numerical experiments. When compared, the proposed method achieves higher calculation accuracy in solving the 6-Degree-of-Freedom rocket-powered landing trajectory problem, while taking into account rocket attitude control. Full article