Limiting Modes of Aircraft Flight: Methods, Algorithms and Results

Introduction
Contents
Abbreviations
1 Onboard Restraint Systems. State of the Issue. Formulation of the Problem
	1.1 Aircraft Accident Analysis
	1.2 Operational and Limiting Flight Modes
	1.3 The Main Types of Restrictions When Piloting an Aircraft
	1.4 The Psychological Characteristics of the Pilot When Flying Close Restrictions
	1.5 Classification of Onboard Systems for Limiting the Limiting Flight Modes. Typical Algorithms for Their Functioning
	1.6 Analysis of Existing Methods for the Synthesis of Systems for Maintaining Constraints. Research Problem Statement
	References
2 The Method of Adaptive Maintenance of Constraints on the Components of the State Vector of a Dynamic System
	2.1 Substantial Problem Statement
	2.2 General Case of Keeping the Constraint
	2.3 Proof of the Analogy of the Method of Maintaining Constraints to the Fundamental Law of Equal-Variable Motion
	2.4 Synthesis of Algorithmic Support for an Adaptive Constraint System for Particular Models of a Dynamic System
		2.4.1 Some Ways to Describe Stationary Constraint Surfaces
		2.4.2 Algorithm for Constraining a Deterministic Linear Continuous Dynamic System
		2.4.3 An Algorithm for Constraining a Deterministic Continuous Controlled Multilevel Dynamical System
	References
3 Algorithms for Adaptive Limitation of Aircraft Flight Parameters
	3.1 Adaptive Limitation of Aircraft Angles of Attack
	3.2 Peculiarities of Maintaining Restrictions on the Observed Parameters of Aircraft Movement
	3.3 Limiting the Roll Angle of the Helicopter
	3.4 Restriction in Space of Two Components of the State Vector by the Example of the Problem of Limiting the Angles of Attack and Slip of an Aircraft
	References
4 Algorithms for Adaptive Limitation of Trajectory Parameters of Aircraft Movement
	4.1 General Case of Limiting the Trajectory of Aircraft Movement in Three-Dimensional State Space
		4.1.1 Substantial Problem Statement
		4.1.2 Object Model and Constraint Surfaces
		4.1.3 Derivation of the Calculated Dependencies of the Limiting Algorithm
	4.2 Particular Problems of Limiting the Trajectory Parameters of Movement in the Vertical and Horizontal Planes
		4.2.1 Aircraft Drift in the Vertical Plane
		4.2.2 Aircraft Drift in the Horizontal Plane
	4.3 Synthesis of Algorithms for Maintaining Limitations Within the Range of Altitudes and Flight Speeds
	4.4 Features of Maintaining Non-Stationary Constraints
	References
5 Aircraft Drift Away from Limiting Surfaces Along Programmed Trajectories
	5.1 Substantial Problem Statement
	5.2 Algorithms for Calculating the Angles of the Aircraft Position in Space in the Case Movement It Away from an Obstacle
	5.3 Conditions for the Activation of «Withdrawal» Mode
	5.4 Formation of Controls
	5.5 Solving Private Problems of Aircraft Evacuation from Obstacles
		5.5.1 Vertical Wall
		5.5.2 Inclined Plane
		5.5.3 Comparative Analysis of Algorithm «Withdrawal»
	References
6 Method and Algorithms for Direct Optimization of the Movement of a Damaged Aircraft
	6.1 Analysis of the Main Prerequisites for Creating a Method of Direct Optimization
	6.2 A Loose Proof of the Correspondence of the Principle of Variation of the Derivative Function of an Arbitrary Curve to the Necessary Optimality Condition
	6.3 Development of the Main Provisions of the Method of Direct Optimization of the Motion of Dynamic Systems
		6.3.1 General Formulation of Optimal Control Problems and Determination of the Sequence of their Solution in the Method of Direct Optimization of Dynamic Systems
		6.3.2 Level-by-Level Decomposition of the Mathematical Model of the Control Object
		6.3.3 The Main Provisions of the Method of Direct Optimization
		6.3.4 Organization of the Procedure for Maintaining the Restrictions on Coordinates of State and Control Vectors
		6.3.5 The Procedure for Optimizing the Basic Trajectory Movement of Aircraft
	6.4 Estimation of the Reliability of the Method of Direct Optimization Using Examples of Solving the Simplest Optimal Control Problems
	6.5 Synthesis of the Laws of Control of the Pilot Circuit Based on the Method of Direct Optimization
	6.6 Technique and Features of Aircraft Thrust Vector Control
		6.6.1 Aircraft Thrust Vector Control Algorithm
		6.6.2 Analysis of the Performance of the Thrust Vector Control Algorithm
	6.7 Extended Version of the Method of Direct Optimization
	References