Optimization Of Nonlinear Systems Research Articles

Measurement and optimization of nonlinear damping systems for agricultural engineering vehicle cab

The issue of nonlinear dampness in the cab of agricultural engineering vehicles is examined by analyzing the vibration reduction system of a specific agricultural loader. Firstly, the specific loader was tested under different conditions. Then, the nonlinear vibration reduction system model of the cab–seat–human body is established by using the measured frame vibration signal as input. Finally, the multi–objective genetic algorithm is used to optimize the root mean square (RMS) value of vertical acceleration of the cab and seat. The test results show that the seat vibration is significantly greater than the acceleration of the cab floor under driving and working conditions, so the seat vibration is amplified and the seat parameter setting is unreasonable; the engine and the working device are also an important part of the cab vibration source, in addition to the uneven road surface. Comparing the RMS values of the vertical acceleration of the cab and seat, which were calculated by the model and obtained from the vehicle test, the error does not exceed 6%, indicating that the model’s accuracy meets the requirement. The vehicle experiment proves that the RMS value of the vertical acceleration of the cab and seat is reduced by 16% and 53%, respectively, after optimization. This study provides a theoretical basis for the design of the damping system for the cab of agricultural engineering vehicles.

Finite-time/fixed-time distributed optimization for nonlinear multi-agent systems with time-varying cost function

Distributed optimization, combining cooperative control and optimization objectives, is vital for practical applications. While current research predominantly focuses on linear multi-agent systems, the real-world demands often involve nonlinear systems with finite or fixed time constraints. This paper addresses the finite-time/fixed-time distributed optimization for nonlinear multi-agent systems with time-varying cost function. Under appropriate assumptions, we propose a finite-time distributed protocol and a fixed-time distributed protocol for the nonlinear multi-agent systems to ensure all agents achieve consensus and minimize the time-varying cost function, relaxing the conditions for strong convexity and bounded gradient difference of the cost function. Simulation experiments validate the effectiveness of these distributed protocols.

Research on Electric Oil-Pneumatic Active Suspension Based on Fractional-Order PID Position Control.

In this study, an electric oil and gas actuator based on fractional-order PID position feedback control is proposed, through which the damping coefficient of the suspension system is adjusted to realize the active control of the suspension. An FOPID algorithm is used to control the motor's rotational angle to realize the damping adjustment of the suspension system. In this process, the road roughness is collected by the sensors as the criterion of damping adjustment, and the particle swarm algorithm is utilized to find the optimal objective function under different road surface slopes, to obtain the optimal cornering value. According to the mathematical and physical model of the suspension system, the simulation model and the corresponding test platform of this type of suspension system are built. The simulation and experimental results show that the simulation results of the fractional-order nonlinear suspension model are closer to the actual experimental values than those of the traditional linear suspension model, and the accuracy of each performance index is improved by more than 18.5%. The designed active suspension system optimizes the body acceleration, suspension dynamic deflection, and tire dynamic load to 89.8%, 56.7%, and 73.4% of the passive suspension, respectively. It is worth noting that, compared to traditional PID control circuits, the FOPID control circuit designed for motors has an improved control performance. This study provides an effective theoretical and empirical basis for the control and optimization of fractional-order nonlinear suspension systems.

Sequential simulated annealing for life-cycle optimization of nonlinear stochastic systems via arbitrary polynomial chaos expansion

Quantifying the uncertainties of engineering systems modeled as nonlinear oscillators subject to random excitation is a theoretically complex and computationally demanding task. Consequently, finding an optimal design of such systems considering their life-cycle performance is prohibitive with Monte Carlo simulation methods. In this paper, an efficient performance-based design optimization approach is developed for finding the optimal parameters of engineering systems modeled as nonlinear/hysteretic oscillators subject to stationary and non-stationary excitation. This novel approach utilizes an arbitrary polynomial chaos expansion to estimate the expected cost of failure without performing a computationally expensive integration over the hazard levels. Moreover, we introduce a novel sequential heuristic optimization scheme based on simulated annealing to minimize the total expected cost over the structure life-cycle. Three examples are included in the paper to assess the developed optimization scheme. First, we use the developed framework to optimize a linear single-degree-of-freedom oscillator subject to broadband excitation. Second, a multi-degree-of-freedom oscillator with cubic nonlinearity in damping and stiffness, subject to stationary broadband excitation, is optimized to show the influence of the problem dimensionality in the optimization process. In the last example, a multi-story reinforced concrete shear building modeled as a multi-degree-of-freedom Bouc-Wen oscillator with stiffness and strength degradation and subject to multi-hazards modeled as stationary (wind excitation) and non-stationary (earthquake) stochastic processes, is optimized.

Fixed-Time Distributed Time-Varying Optimization for Nonlinear Fractional-Order Multiagent Systems with Unbalanced Digraphs

This paper investigates the problem of fixed-time distributed time-varying optimization of a nonlinear fractional-order multiagent system (FOMAS) over a weight-unbalanced directed graph (digraph), where the heterogeneous unknown nonlinear functions and disturbances are involved. The aim is to cooperatively minimize a convex time-varying global cost function produced by a sum of time-varying local cost functions within a fixed time, where each time-varying local cost function does not have to be convex. Using a three-step design procedure, a fully distributed fixed-time optimization algorithm is constructed to achieve the objective. The first step is to design a fully distributed fixed-time estimator to estimate some centralized optimization terms within a fixed time T0. The second step is to develop a novel discontinuous fixed-time sliding mode algorithm with nominal controller to derive all the agents to the sliding-mode surface within a fixed time T1, and meanwhile the dynamics of each agent is described by a single-integrator MAS with nominal controller. In the third step, a novel estimator-based fully distributed fixed-time nominal controller for the single-integrator MAS is presented to guarantee all agents reach consensus within a fixed time T2, and afterwards minimize the convex time-varying global cost function within a fixed time T3. The upper bound of each fixed time Tm(m=0,1,2,3) is given explicitly, which is independent of the initial states. Finally, a numerical example is provided to validate the results.

H2-powered aviation – Design and economics of green LH2 supply for airports

The economic competitiveness of hydrogen-powered aviation highly depends on the supply costs of green liquid hydrogen to enable true-zero CO2 flying. This study uses non-linear energy system optimization to analyze three main liquid hydrogen (LH2) supply pathways for five locations.Final liquid hydrogen costs at the dispenser could reach 2.04USD/kgLH2 in a 2050 base case scenario for locations with strong renewable energy source conditions. This could lead to cost-competitive flying with hydrogen.Reflecting techno-economic uncertainties in two additional scenarios, the liquid hydrogen cost span at all five airport locations ranges between 1.37 and 3.48USD/kgLH2, if hydrogen import options from larger hydrogen markets are also available. Import setups are of special importance for airports with a weaker renewable energy source situation, e.g., selected Central European airports. There, on-site supply might not only be too expensive, but space requirements for renewable energy sources could be too large for feasible implementation in densely populated regions.Furthermore, main costs for liquid hydrogen are caused by renewable energy sources, electrolysis systems, and liquefaction plants. Seven detailed design rules are derived for optimized energy systems for these and the storage components. This and the cost results should help infrastructure planners and general industry and policy players prioritize research and development needs.

Distributed Optimization for Uncertain High-Order Nonlinear Multiagent Systems via Dynamic Gain Approach

In this article, we investigate the distributed output optimization for general uncertain high-order nonlinear multiagent systems (MASs), where nonlinear functions are constrained by a linear growth condition. The dynamic gain approach is utilized to cope with the influence of the unknown optimal solution. First, the distributed optimal coordinators (DOCs) with an adjustable parameter are constructed to steer the generated signals converging to the optimal solution. By developing the iterative design strategy, the dynamic reference-tracking controllers are then designed so that the output of each agent follows the generated value of coordinators, respectively. It is proved that all states are globally bounded, as well as the tracking error between the outputs and optimal solution can be bounded in a finite time by an arbitrarily small constant. Simulation studies demonstrate the validness of the main idea.

INFORM: Inverse Design Methodology for Constrained Multiobjective Optimization

Many system design methods use population-based optimization or a surrogate model for solving constrained multi-objective optimization. When designing a system with multiple objectives and constraints, the designer may first be interested in understanding the trade-offs among different objectives from a small number of simulations. In the next step, the designer may focus on specific regions of interest in the design space near a set of non-dominated solutions to further improve performance on the targeted objectives. This may help make the search process sample-efficient. We propose INFORM: a two-step approach for sample-efficient constrained multi-objective optimization of real-world nonlinear systems. In the first step, we modify a genetic algorithm (GA) to make the design process sample-efficient. We inject candidate solutions into the GA population using inverse design methods instead of determining the candidate solutions for the next generation using only crossover and mutation, as is done in standard GA. We present three types of inverse design techniques based on a (i) neural network verifier, (ii) neural network, and (iii) Gaussian mixture model. The candidate solutions for the next generation are thus a mix of those generated using crossover/mutation and solutions generated using inverse design. At the end of the first step, we obtain a set of non-dominated solutions. In the second step, we choose the regions of interest around the non-dominated solutions to further improve the objective function values using inverse design methods. We demonstrate the efficacy of INFORM through synthesis of nonlinear systems and analog circuits. The experimental results show that INFORM reduces synthesis time by up to 29× and improves the value of the objective function by up to 33% compared to a state-of-the-art baseline design methodology.

Distributed convex optimization of higher order nonlinear uncertain multi-agent systems with switched parameters and topologies

This paper investigates the distributed optimization problem for a class of nonlinear uncertain multi-agent systems with unmeasured states, switched parameters, and directed communication topologies changing in the control process. To achieve the goal of optimizing the global objective function, a penalty function is constructed through making up of a sum of local objective functions and integrating consensus conditions of the multi-agent systems to utilize local and neighboring information. Radial basis function neural-networks and neural-networks state observer are applied to approximate the unknown nonlinear functions and obtain the unmeasured states, respectively. To avoid “explosion of complexity” and obtain derivatives for virtual control functions continuously, dynamic surface control technology is proposed to develop a distributed adaptive backstepping neural network control protocol to ensure that all the agents’ outputs asymptotically reach consensus to the optimal solution of the global objective function. Simulations demonstrate the effectiveness of the proposed control scheme.

Multi-population cooperative teaching–learning-based optimization for nonlinear equation systems

Solving nonlinear equation systems (NESs) requires locating different roots in one run. To effectively deal with NESs, a multi-population cooperative teaching–learning-based optimization, named MCTLBO, is presented. The innovations of MCTLBO are as follows: (i) two niching technique (crowding and improved speciation) are integrated into the algorithm to enhance population diversity; (ii) an adaptive selection scheme is proposed to select the learning rules in the teaching phase; (iii) the new learning rules based on experience learning are developed to promote the search efficiency in the teaching and learning phases. MCTLBO was tested on 30 classical problems and the experimental results show that MCTLBO has better root finding performance than other algorithms. In addition, MCTLBO achieves competitive results in eighteen new test sets.

Distributed optimization for nonlinear multi-agent systems with an upper-triangular structure

This paper proposes a new two-step distributed optimization framework with a low-gain parameter for a class of upper-triangular nonlinear multi-agent systems. Specifically, distributed optimal coordinators are first established to generate signals close to the optimal solution by using the real-time values of gradient functions. Then, reference-tracking controllers are designed to make system outputs converge to the generated signals by coordinators. Correspondingly, system outputs can converge to the optimal solution by choosing the appropriate low-gain parameter. Finally, simulation results illustrate the proposed control scheme.

Hierarchical maximum likelihood identification based on Levenberg–Marquardt and particle swarm optimization for feedback nonlinear systems

This article covers the identification of the feedback nonlinear systems. The parameterized nonlinear identification model involves products of system nonlinear part parameters and system linear part parameters. To deal with these product terms, the hierarchical identification based on maximum likelihood is used to decompose the system into two subsystems. The Levenberg–Marquardt and particle swarm optimization methods are applied for identifying the two subsystems, respectively. For the purpose of enhancing the optimization capability of the basic particle swarm optimization method, some improvement strategies are constructed. Thus, the improved particle swarm optimization algorithm which combines the adaptive feedback, the linearly decreasing method and the mutational operator is applied to adaptively adjust the search strategy and improve the ergodicity. The simulation indicates that the derived estimation is effective because it can obtain high identification accuracy and fast convergence speed when identifying the feedback systems. Besides, the case study demonstrates that the proposed method can be well used to identify the electro-hydraulic-servo position system.

Economic optimization and predictive control for nonlinear systems using Lyapunov based nonlinear cost function design

Optimal control of physical processes depends on the formulation of objective functions and contemplation of appropriate predictive control. In this article, we propose a new framework, to blend the concepts of the Lyapunov-based economic model predictive control (Ly-EMPC) scheme with the novel cost-efficient profit function design. Furthermore, Lyapunov’s stability criteria is employed to verify the existence of duality and optimality for the designed economic stage costs. This method differs from the existing EMPC techniques by implementing Lagrange multipliers in the rotated cost function as a measure of stability. The closed-loop performance using the regularized Ly-EMPC is validated against a standard tracking objective-based nonlinear MPC for three benchmark examples through an econometrics gauge factor. Interestingly, in contrast to tracking NMPC, the proposed Ly-EMPC scheme excels in economic performance, while the formation of nonlinear economic stage cost is conceptually simpler, novel, and practically profitable.

Data‐based learning control for optimization of nonlinear systems

Data‐based learning control for optimization of nonlinear systems

Momentum-Based Distributed Continuous-Time Nonconvex Optimization of Nonlinear Multi-Agent Systems via Timescale Separation

This study addresses the distributed nonconvex optimization problem for nonlinear multi-agent systems over a weight-balanced and quasi-strongly connected graph. The purpose is to steer all agents to the optimum of a given global objective function with inputs and outputs on the basis of the actual partial information related to the input and output. Novel momentum-based distributed optimal coordinators are designed to achieve this objective, and the local objective functions should be analytic to replace its convexity. An interconnected system with different timescales is established by converting the overall closed-loop system involving the module of momentum-based distributed optimal coordinators and nonlinear multi-agent systems. The singular perturbation approach is applied to deal with the overall interconnected closed-loop system by timescale separation. A numerical example and an application example with four firefighting unmanned aerial vehicles (UAVs) verify the superiority and effectiveness of the proposed distributed method and extended algorithms. Three momentum-based gradient descent algorithms (basic momentum-based, momentum-based Newton, and projected momentum-based gradient flows) are compared and analyzed.

Multiobjective Dynamic Optimization of Nonlinear Systems With Path Constraints

In this article, two algorithms are proposed to solve multiobjective path-constrained dynamic optimization problems. In each algorithm, an adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -constraint method is employed to solve the multiobjective dynamic optimization problems (MODOPs) with path constraints in two iterative loops. In the outer loop, the adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -constraint method adaptively adjusts the choice of the parameters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> , which transfers MODOP into a sequence of single-objective dynamic optimization problems (SODOPs) with extra inequality constraints. In the inner loop, two different algorithms are used to solve the single-objective optimization problems. The first algorithm guarantees that the path constraints can be satisfied with any finite prescribed tolerance by replacing path constraints with a finite number of point constraints. Furthermore, the second algorithm guarantees that the path constraints are rigorously satisfied by enforcing the path constraints at a limited number of time points and by restricting the right-hand side of the path constraints. The proposed algorithms are proven to converge within finite iterations. The effectiveness of the algorithms is verified via numerical studies, along with a comparison to a state-of-the-art algorithm.

Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty

In this article, we present generalized polynomial chaos-based sequential convex programming (gPC-SCP) to compute a suboptimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion planning for robotic systems under uncertainty. The gPC-SCP method involves two steps. The first step is to derive a surrogate problem of deterministic nonlinear optimal control (DNOC) with convex constraints by using gPC expansion and the distributionally robust convex subset of the chance constraints. The second step is to solve the DNOC problem using sequential convex programming for trajectory generation and control. We prove that in the unconstrained case, the optimal value of the DNOC converges to that of SNOC asymptotically and that any feasible solution of the constrained DNOC is a feasible solution of the chance-constrained SNOC. We also present the predictor–corrector extension (gPC-SCP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\text{PC}$</tex-math></inline-formula> ) for real-time motion trajectory generation in the presence of stochastic uncertainty. In the gPC-SCP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\text{PC}$</tex-math></inline-formula> method, we first predict the uncertainty using the gPC method and then optimize the motion plan to accommodate the uncertainty. We empirically demonstrate the efficacy of the gPC-SCP and the gPC-SCP <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^\text{PC}$</tex-math></inline-formula> methods for the following two test cases: first, collision checking under uncertainty in actuation and physical parameters and second, collision checking with stochastic obstacle model for 3DOF and 6DOF robotic systems. We validate the effectiveness of the gPC-SCP method on the 3DOF robotic spacecraft testbed.

Nonlinear system control analysis and optimization using advanced Pigeon-Inspired optimization algorithm

The Pigeon-Inspired optimization (PIO) algorithm is a novel intelligent optimization algorithm inspired by birds’ behavior as their travel. This; behavior modeled to be used for solving many optimization problems in different fields. However; it always suffers from unstable behavior when used with nonlinear; time-varying systems. In; this paper, this algorithm is adapted to calculate the optimum controller gains for roll and pitch channels in a guided tactical missile. The; vehicle model is presented in a nonlinear; form and then shown in a linearized form for the sake of an autopilot design. The PIO; algorithm is supported and accompanied by an adaptive algorithm to determine the initial states and constraints for the PIO algorithm to enhance the behavior of the optimization algorithm to speed up the convergence rate to reach an optimum and feasible solution. Also; an estimation function is incorporated to estimate model parameters variation such as dynamic pressure, stability derivatives, and mass properties. Meanwhile; a comparative analysis is carried out with original PIO and particle swarm optimization algorithms, utilizing a non-linear; model with the presence of noise source and disturbance to ensure the ability of the algorithm to make the autopilot robust and stable against several sources of uncertainties.

A framework of adaptive fuzzy control and optimization for nonlinear systems with output constraints

This paper presents a framework for adaptive fuzzy control and optimization of nonlinear systems subject to uncertainties and disturbances. The barrier Lyapunov function (BLF) technique was adopted to determine output constraints. To enhance the tracking performance of the system, fuzzy logic systems (FLSs) were introduced to approximate nonlinear terms. Subsequently, a combination of Bayesian optimization and particle swarm optimization (BO-PSO) was employed for gains optimization to further improve the control performance. Furthermore, the multilayer neural networks (MNNs) were applied as surrogate models of nonlinear systems with interval parameters to improve the computational efficiency of the optimization process. Finally, two simulations were conducted to demonstrate the effectiveness of the proposed framework.

Distributed optimization for uncertain nonlinear interconnected multi-agent systems

Distributed optimization for uncertain nonlinear interconnected multi-agent systems is considered in this paper. The objective is to design distributed algorithms by using local information such that all the agents’ outputs converge to the global optimal output. The problem is challenging due to unknown modeling uncertainties and nonlinear interconnections. First, a distributed algorithm composed of a distributed state observer and a distributed optimal output observer is presented for heterogeneous outputs. Next, it is shown that the objective can be achieved by employing solely a distributed optimal output observer if the agents’ outputs are homogeneous. Finally, the algorithms’ effectiveness is validated by an electrical power system composed of four-machine subsystems.