Abstract This paper discusses multi-agent path navigation in unknown environments. It is a challenging task to design an effective communication-based algorithm with minimal error, which would ensure secure navigation of multi-agent paths under complex circumstances, reduce the length of the travelled path, and minimize the runtime. A leader agent path navigation (LAPN) algorithm is proposed in this paper for multi-agent communication. The obstacle avoidance mechanism is used in the first part of the algorithm. The execution time of the algorithm is influenced by the process of leader-to-follower path update, since the updating process determines how quickly the followers receive corrected trajectories. One leader and two follower agents were considered in simulation environments to establish the feasibility of the algorithm. The LAPN algorithm achieves an average percentage deviation, calculated as the relative difference from the ideal straight-line path of 2.82% in travel time and 31% in path length, showing satisfactory navigation efficiency under obstacle-constrained conditions.
Abstract The paper addresses the Two-Constraint Binary Knapsack Problem. It is assumed that some of the problem coefficients are the realizations of mutually independent random variables. Asymptotic probabilistic properties of selected problem characteristics are investigated for special cases of Lagrange multipliers with small, moderate and mixed values.
This study introduces an observer-based dual strategy for optimizing block mode placement in matrix polynomial control systems, focusing on improving stability and performance in multivariable feedback applications. It introduces two approaches: a static state feedback compensator for a challenging Bidirectional Inductive Power Transfer (IPT) System, and a dynamic observer-based output feedback compensator for a defensive air-to-surface missile control problem. Both designs exploit the Grey Wolf Optimizer to solve the nonlinear convex optimization, associated with block mode selection. The dynamic plan employs Luenberger observer principles for unmeasured state estimation, ensuring system reliability through strict observability conditions. Simulation results reveal that the proposed optimal placement methods enhance tracking, boost stability margins, and substantially minimize control effort. Overall, this methodology offers an effective frame-work for robust controller design and state estimation across disparate, complex dynamic systems, while reducing computational burden and improving control efficiency.
We use first- and second-order approximations to establish necessary and suffcient optimality conditions for nonsmooth generalized bilevel optimization problems with variational inequality constraints. To transform the hierarchical problem into a single-level optimization problem, we employ two approaches: the gap function reformulation and the KKT reformulation. We compare these approaches and provide examples to illustrate the applicability of the results.
The article is concerned with the nonlinear optimal control problem of two cable-driven 3-DOF robotic cranes. Such cranes can be used in ship maintenance and repair. These are underactuated robotic systems comprising a 2-cable driven cart with a payload suspended from it. Such robotic mechanisms have three degrees of freedom and can move in the entire 2D vertical plane. Using Euler-Lagrange analysis the state-space model of the two cable-driven 3-DOF robotic crane is obtained. It is also proven that this dynamic model is differentially flat. Next, to solve the associated nonlinear optimal control problem, the dynamic model of the two cable-driven 3-DOF robotic crane undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the crane an optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Besides, the method avoids change of state variables and state-space model transformations and the control inputs it computes are applied directly on the initial nonlinear state-space model of the crane.
