The major premise of deterministic artificial intelligence (D.A.I.) is to assert deterministic self-awareness statements based in either the physics of the underlying problem or system identification to establish governing differential equations. The key distinction between D.A.I. and ubiquitous stochastic methods for artificial intelligence is the adoption of first principles whenever able (in every instance available). One benefit of applying artificial intelligence principles over ubiquitous methods is the ease of the approach once the re-parameterization is derived, as done here. While the method is deterministic, researchers need only understand linear regression to understand the optimality of both self-awareness and learning. The approach necessitates full (autonomous) expression of a desired trajectory. Inspired by the exponential solution of ordinary differential equations and Euler’s expression of exponential solutions in terms of sinusoidal functions, desired trajectories will be formulated using such functions. Deterministic self-awareness statements, using the autonomous expression of desired trajectories with buoyancy control neglected, are asserted to control underwater vehicles in ideal cases only, while application to real-world deleterious effects is reserved for future study due to the length of this manuscript. In totality, the proposed methodology automates control and learning merely necessitating very simple user inputs, namely desired initial and final states and desired initial and final time, while tuning is eliminated completely.
Nonlinear systems are typically linearized to permit linear feedback control design, but, in some systems, the nonlinearities are so strong that their performance is called chaotic, and linear control designs can be rendered ineffective. One famous example is the van der Pol equation of oscillatory circuits. This study investigates the control design for the forced van der Pol equation using simulations of various control designs for iterated initial conditions. The results of the study highlight that even optimal linear, time-invariant (LTI) control is unable to control the nonlinear van der Pol equation, but idealized nonlinear feedforward control performs quite well after an initial transient effect of the initial conditions. Perhaps the greatest strength of ideal nonlinear control is shown to be the simplicity of analysis. Merely equate coefficients order-of-differentiation insures trajectory tracking in steady-state (following dissipation of transient effects of initial conditions), meanwhile the solution of the time-invariant linear-quadratic optimal control problem with infinite time horizon is needed to reveal constant control gains for a linear-quadratic regulator. Since analytical development is so easy for ideal nonlinear control, this article focuses on numerical demonstrations of trajectory tracking error.
This manuscript will explore and analyze the effects of different paradigms for the control of rigid body motion mechanics. The experimental setup will include deterministic artificial intelligence composed of optimal self-awareness statements together with a novel, optimal learning algorithm, and these will be re-parameterized as ideal nonlinear feedforward and feedback evaluated within a Simulink simulation. Comparison is made to a custom proportional, derivative, integral controller (modified versions of classical proportional-integral-derivative control) implemented as a feedback control with a specific term to account for the nonlinear coupled motion. Consistent proportional, derivative, and integral gains were used throughout the duration of the experiments. The simulation results will show that akin feedforward control, deterministic self-awareness statements lack an error correction mechanism, relying on learning (which stands in place of feedback control), and the proposed combination of optimal self-awareness statements and a newly demonstrated analytically optimal learning yielded the highest accuracy with the lowest execution time. This highlights the potential effectiveness of a learning control system.
Automatic controls refer to the application of control theory to regulate systems or processes without human intervention, and the notion is often usefully applied to space applications. A key part of controlling flexible space robotics is the control-structures interaction of a light, flexible structure whose first resonant modes lie within the bandwidth of the controller. In this instance, the designed-control excites the problematic resonances of the highly flexible structure. This manuscript reveals a novel compensator capable of minimum-time performance of an in-plane maneuver with zero residual vibration (ZV) and zero residual vibration-derivative (ZVD) at the end of the maneuver. The novel compensator has a whiplash nature of first commanding maneuver states in the opposite direction of the desired end state. For a flexible spacecraft simulator (FSS) free-floating planar robotic arm, this paper will first derive the model of the flexible system in detail from first principles. Hamilton's principle is augmented with the adjoint equation to produce the Euler-Lagrange equation which is manipulated to prove equivalence with Newton's law. Extensive efforts are expended modeling the free-free vibration equations of the flexible system, and this extensive modeling yields an unexpected control profile-a whiplash compensator. Equations of motion are derived using both the Euler-Lagrange method and Newton's law as validation. Variables are then scaled for efficient computation. Next, general purposed pseudospectral optimization software is used to seek an optimal control, proceeding afterwards to validate optimality via six theoretical optimization necessary conditions: (1) Hamiltonian minimization condition; (2) adjoint equations; (3) terminal transversality condition; (4) Hamiltonian final value condition; (5) Hamiltonian evolution equation; and lastly (6) Bellman's principle. The results are novel and unique in that they initially command full control in the opposite direction from the desired end state, while no such results are seen using classical control methods including classical methods augmented with structural filters typically employed for controlling highly flexible multi-body systems. The manuscript also opens an interesting question of what to declare when the six optimality necessary conditions are not necessarily in agreement (we choose here not to declare finding the optimal control, instead calling it suboptimal).Aerospace 2019, 6, 93 2 of 18 highly flexible structure. In order to optimize the control of such challenging systems, a brief review of mechanics and ubiquitous control techniques is warranted.Mechanical motion of mass in six degrees of freedom is completely described by separate treatment of three degrees of freedom of translation plus three additional degrees of freedom of rotation as articulated in the year 1830 [1] and expanded and modernized over the following two centuries [2][3][4][5][6][7][8][9][10][11][12][13]. Translational degrees of freedom are governed by Newton's law, whil...
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