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In the guidance literature, minimizing miss distance along with optimizing the energy usage had been an objective for several decades. In current day applications, additional terminal performance such as impact angle and impact time are of paramount importance. These terminal constraints increase warhead effectiveness and survivability of the interceptor. This thesis contributes to the design of guidance laws addressing terminal constraints such as impact angle, impact time, and both impact time as well as impact angle, in addition to interception of targets. In the first part of the thesis, the guidance laws which ensure the alignment of the interceptor at a desired impact angle within a finite time is proposed using different variants of sliding mode control(SMC).The impact angle is first redefined in terms of line-of-sight angle and then the impact angle problem is converted to a simpler problem of controlling line-of-sight angle and their rates. The sliding mode capturability and interpretation of the guidance laws are presented. In order to cater to very large heading angle errors, which give rise to negative closing speed initially, modifications to the guidance laws are also suggested. The modifications to the guidance laws for avoiding singularities, which may be encountered during implementation, due to the inherent nature of terminal SMC, are suggested. However, the guidance laws, which alleviates the possibility of such singularities completely, are also designed by using non singular terminal SMC. The two loop guidance and control, for a skid-to-turn cruciform interceptor in the pitch plane, is also proposed with an autopilot designed using the concept of dynamic SMC. The guidance laws addressing impact angle constraint for three dimensional scenarios are also presented. Unlike the usual approach of decoupling the three dimensional engagement in to two mutually orthogonal planar engagements, the guidance laws are derived using coupled engagement dynamics. These guidance laws are designed using conventional and non singular terminal SMC and provide asymptotic and finite time alignment of the intercept or to the desired impact angles, respectively. Next, the SMC based guidance laws which ensure the interception of targets at pre-specified impact times is proposed in this thesis. The guidance law is first designed for stationary targets and then extended to constant velocity targets using the notion of predicted interception point. A switching surface is designed using the concepts of collision course and time-to-go with non-linear engagement dynamics and its role in achieving the objectives is also discussed. In order to account for large heading angle errors and even for negative initial closing speeds, different methods of estimation of time-to-go, resulting in two different guidance laws, are used. Unlike the existing guidance laws, the proposed guidance laws achieve an impact time even less than its initially estimated value. The flexibility in selecting a desired impact time is also exploited using the maximum available acceleration information. A cooperative salvo attack strategy, based on the proposed impact time guidance law, with a desired impact time chosen in real time using a centralized coordination algorithm, is proposed for stationary targets. The coordination manager determines a common impact time based on time-to-goof the interceptors, by minimizing the total switching surface deviations which in turn reduces the control effort. The thesis also proposes a SMC based guidance strategy which addresses impact angle and impact time constraints simultaneously. This guidance scheme is based on switching between impact time and impact angle guidance laws based on certain conditions. Unlike existing impact time guidance laws, the proposed guidance strategy takes into account the curvature of the trajectory due to the impact angle requirement. The interceptor first corrects its course to nullify the impact time error and then aims to achieve interception with desired impact angle. In order to reduce the transitions between the two guidance laws, a novel hysteresis loop is introduced in the switching conditions. Initially stationary targets are considered, and later the same guidance scheme is extended to constant velocity targets using the notion of predicted interception point. Theclaimsofalltheguidancelawsarevalidatedwithextensivesimulationsandtheir performances are compared with existing guidance laws. Although all the guidance laws derived in the thesis are based on the assumption of constant speed interceptors, their performances are evaluated with a time-varying speed interceptor model, subjected to aerodynamic conditions, to validate their efficacy. The implementation of impact time guidance on time-varying speed interceptors is a formidable challenge in the guidance literature. Such implementations have also been presented in the thesis after introducing the notion of average speed and shown to yield satisfactory performance.

Guidance is defined as the determination of a strategy for following a nominal path in the presence of o-nominal conditions, disturbances and uncertainties, and the strategy employed is called a guidance law. Variants of Proportional Navigation (PN), such as True Proportional Navigation (TPN) and Pure Proportional Navigation (PPN), have been studied extensively in the literature on tactical missile guidance. In the absence of target maneuvers, in a linear interceptor guidance problem, TPN was shown to be optimal. However, the standard PN class of guidance laws per se does not show good performance against maneuvering targets, and was found to be eective in intercepting a maneuvering target only from a restrictive set of initial geometries. Also, since these guidance laws were eectively designed for lower speed targets, they show a degraded performance when applied against higher speed targets. However, in the current defense scenario, two classes of agile targets, which are capable of continuous maneuver, and/or of much higher speed than the interceptor, are a reality. This thesis presents analysis of several variants of PN class of guidance laws against these two classes of agile targets. In the literature, an augmentation of the TPN guidance law, termed as Augmented Proportional Navigation (APN), was shown to be optimal in linearized engagement framework. The present work proposes an augmentation of the PPN guidance law, which is more realistic than TPN for an aerodynamically controlled interceptor, and an-alyzes its capturability in fully nonlinear framework, and develops sauciest conditions on speed ratio, navigation gain and augmentation parameter to ensure that all possible initial engagement geometries are included in the capture zone when applied against a target executing piecewise continuous maneuver. The thesis also obtains the capture zone in the relative velocity space for augmented PPN guidance law. In the literature, a novel guidance law was proposed for the interception of higher speed targets in planar engagement by using a negative navigation gain instead of the standard positive one, and was termed as Retro-PN. It was shown that even though the Retro-PN guided interceptor takes more time than PN guided one in achieving successful interception, Retro-PN performs significantly better than the classical PN law, in terms of capturability, lateral acceleration demand, and closing velocity, when used against higher speed targets. The thesis analyzes Retro-PN guidance law in 3-D engagement geometries to yield the complete capture zone of interceptors guided by Retro-PN guidance philosophy, and derives necessary and sucient conditions for the capture of higher speed non-maneuvering targets with and without a constraint on finiteness of lateral acceleration. Terminal impact angle control is crucial for enhancement of warhead eectiveness. In the literature, this problem has been addressed mostly in the context of targets with lower speeds than the interceptor. The thesis analyzes the performance of a composite PN guidance law, that uses standard PPN and the Retro-PN guidance laws based on initial engagement geometry and requirement of impact angle, against higher speed non-maneuvering targets. Then, to expand the set of achievable impact angles, it proposes a modified composite PN guidance scheme, and analyzes the same. For implementation of many modern guidance laws, a good estimate of time-to-go is essential. This requirement is especially severe in case of impact time constrained en-gagement scenarios. To this end, an ecient and fast time-to-go estimation algorithm for generic 3-D engagement is required. Two time-to-go estimation algorithms are presented and analyzed in this work for the engagement of a PPN or Retro-PN guided interceptor and a higher speed target. The first one is a closed form approximation of time-to-go in terms of range, nominal closing speed and an indicator of heading error, and the second one is a numerical recursive time-to-go estimation algorithm. To improve the odds of intercepting an intelligent target and destroying it, a salvo attack of two or more interceptors could be considered as a viable option. Moreover, this simultaneous salvo attack can also be further improved in eciency by incorporating the shoot-look-shoot approach in making a decision about launching interceptors. This can be considered as the first step towards a layered defense system, which has been described in the literature as a potentially eective strategy against short range or long range ballistic threat. To this end, the present work proposes two PPN and Retro-PN based guidance strategies for achieving simultaneous salvo attack on a higher speed non-maneuvering target. For the implementation of the same the numerical recursive time-to-go estimation technique proposed in this work is utilized

Autonomous aerial vehicles like missiles and unmanned aerial vehicles (UAVs) have attracted various military and civilian applications. The primary guidance objective of any autonomous vehicle is to reach the desired destination point (target or waypoint). However, many practical engagements impose additional constraints like minimum control effort, a desired final velocity direction or a predefined engagement time. This thesis addresses engagement time constrained guidance problems pertaining to missiles and UAVs. The first part of the thesis discusses a nonlinear guidance law for impact time control of missiles against stationary target. The guidance law is designed with a particular choice of missile heading error variation as a function of ran to-target. The proposed heading error variation leads to an exact closed-form expression for the impact time. controlling the impact time, a closed-form relation is derived relating the control parameter to the desired impact time. A new Lyapunov based guidance law with a monotonically decreasing lateral acceleration is proposed in the next part of the thesis. An exact expression for impact time with minimum and maximum achievable impact times is derived. A control parameter is proposed with a closed-form relationship to the desired impact time. Using the concept of predicted interception point, the two guidance laws are extended for impact time control against non-maneuvering and moving targets. The proposed guidance models are extended to three-dimensional engagements by deducing yaw and pitch lateral accelerations satisfying the desired heading error profile. Extensive simulation studies are carried out for single missile and salvo attack scenarios. The last part of the thesis presents a guidance methodology governing the arrival time of a UAV at a waypoint. A specific arrival angle is considered as an additional constraint. The arrival constraints are satisfied by varying the navigation gain of the proportional navigation guidance law. The methodology is applied for simultaneous and sequential arrival of UAVs at a waypoint.

In this thesis the cubic spline guidance law and its variants are derived. A detailed analysis is carried out to find the initial conditions for successful interception. The results are applied to three dimensional guidance design and for solving waypoint following problems. The basic cubic spline guidance law is derived for intercepting a stationary target at a desired impact angle in a surface-to-surface engagement scenario. The guidance law is obtained using an inverse method, from a cubic spline curve based trajectory. For overcoming the drawbacks of the basic cubic spline guidance law, it is modified by introducing an additional parameter. This modification has an interesting feature that the guidance command can be obtained using a single cubic spline polynomial even for impact angles greater than π/2, while resulting in substantial improvement in the guidance performance in terms of lateral acceleration demand and length of the trajectory. For imparting robustness to the cubic spline guidance law, in the presence of uncertainties and acceleration saturation, an explicit guidance expression is also derived. A comprehensive capturability study of the proposed guidance law is carried out. The capturability for the cubic spline guidance law is defined in terms of the set of all feasible initial conditions for successful interception. This set is analytically derived and its dependence on various factors, such as initial engagement geometry and interceptor capability, are also established. The basic cubic spline guidance and its variants are also derived for a three dimen- sional scenario. The novelty of the present work lies in the particular representation of the three dimensional cubic spline curve and the adoption of the analytical results available for two dimensional cubic spline guidance law. This enables selection of the boundary condition at launch for given terminal boundary condition and also in avoiding the singularities associated with the inverse method based guidance laws. For establishing the feasibility of the guidance laws in the real world, the rigid body dynamics of the interceptor is presented as a 6 degrees-of-freedom model. Further, using a simplified model, elementary autopilots are also designed. The successful interception of the target in the presence of the rigid body dynamics proves practical applicability of the cubic spline based guidance laws. Finally, the theory developed in the first part of the thesis is applied to solve the waypoint following problem. A smooth path is designed for transition of vehicle velocity from incoming to outgoing direction. The approach developed is similar to Dubins’ path, as it comprises line–cubic spline–line segments. The important feature of this method is that the cubic spline segments are fitted such that the path curvature is bounded by a pre-specified constrained value and the acceleration demand for following the smooth path obtained by this method, gradually increases to the maximum value and then decreases. This property is advantageous from a practical point of view. All the results obtained are verified with the help of numerical simulations which are included in the thesis. The proposed cubic spline guidance law is conceptually simple, does not use linearised kinematic equations, is independent of time-to-go es- timates, and is also computationally inexpensive.

In this thesis, the problem of intercepting highly manoeuvrable threats using seeker-less interceptors that operate in the command guidance mode, is addressed. These systems are more prone to estimation errors than standard seeker-based systems. Several non-linear and optimal estimation and guidance concepts are presented in this thesis for interception of randomly maneuvering targets by seeker-less interceptors. The key contributions of the thesis can be broadly categorized into six groups, namely (i) an optimal selection of bank of lters in interactive multiple model (IMM) scheme to cater to various maneuvers that are expected during the end-game, (ii) an innovative algorithm to reduce chattering phenomenon and formulate effective guidance algorithm based on 'differential game guidance law' (modi ed DGL), (iii) IMM/DGL and IMM/modified DGL based integrated estimation/guidance (IEG) strategy, (iv) sensitivity and robustness analysis of Kalman lters and ne tuning of lters in filter bank using innovation covariance, (v) Performance of tuned IMM/PN, tuned IMM/DGL and tuned IMM/modi ed DGL against various target maneuvers, (vi) Performance comparison with realistic missile model. An innovative generalized state estimation formulation has been proposed in this the-sis for accurately estimating the states of incoming high speed randomly maneuvering targets. The IMM scheme and an optimal selection of lters, to cater to various maneu-vers that are expected during the end-game, is described in detail. The key advantage of this formulation is that it is generic and can capture evasive target maneuver as well as straight moving targets in a uni ed framework without any change of target model and tuning parameters. In this thesis, a game optimal guidance law is described in detail for 2D and 3D engagements. The performance of the differential game based guidance law (DGL) is compared with conventional Proportional Navigation (PN) guidance law, especially for 3D interception scenarios. An innovative chatter removal algorithm is introduced by modifying the differential game based guidance law (modified DGL). In this algorithm, chattering is reduced to the maximum extent possible by introducing a boundary layer around the switching surface and using a continuous control within the boundary layer. The thesis presents performance of the modified DGL algorithm against PN and DGL, through a comparison of miss distances and achieved accelerations. Simulation results are also presented for varying fiight path angle errors. Apart from the guidance logic, two novel ideas have been presented following the evolving "integrated estimation and guidance" philosophy. In the rst approach, an in-tegrated estimation/guidance (IEG) algorithm that integrates IMM estimator with DGL law (IMM/DGL), is proposed for seeker-less interception. In this interception scenario, the target performs an evasive bang-bang maneuver, while the sensor has noisy measure-ments and the interceptor is subject to an acceleration bound. The guidance parameters (i.e., the lateral acceleration commands) are computed with the help of zero e ort miss distance. The thesis presents the performance of the IEG algorithm against combined IMM with PN (IMM/PN), through a comparison of miss distances. In the second ap-proach, a novel modi ed IEG algorithm composed of IMM estimator and modi ed DGL guidance law is introduced to eliminate the chattering phenomenon. Results from both of these integrated approaches are quite promising. Monte Carlo simulation results re-veal that modi ed IEG algorithm achieves better homing performance, even if the target maneuver model is unknown to the estimator. These results and their analysis o er an insight to the interception process and the proposed algorithms. The selection of lter tuning parameters puts forward a major challenge for scien-tists and engineers. Two recently developed metrics, based on innovation covariance, are incorporated for determining the filter tuning parameters. For predicting the proper combination of the lter tuning parameters, the metrics are evaluated for a 3D interception problem. A detailed sensitivity and robustness analysis is carried out for each type of Kalman lters. Optimal and tuned Kalman lters are selected in the IMM con guration to cater to various maneuvers that are expected during the end-game. In the interception scenario examined in this thesis, the target performs various types of maneuvers, while the sensor has noisy measurements and the interceptor is subject to acceleration bound. The tuned IMM serves as a basis for synthesis of e cient lters for tracking maneuvering targets and reducing estimation errors. A numerical study is provided which demonstrates the performance and viability of tuned IMM/modi ed DGL based modi ed IEG strategy. In this thesis, comparison is also performed between tuned IMM/PN, tuned IMM/DGL and tuned IMM/modi ed DGL in integrated estimation/guidance scheme. The results are illustrated by an extensive Monte Carlo simulation study in the presence of estimation errors. Simulation results are also presented for end game maneuvers and varying light path angle errors . Numerical simulations to study the aerodynamic e ects on integrated estimation/ guidance structure and its e ect on performance of guidance laws are presented. A detailed comparison is also performed between tuned IMM/PN, tuned IMM/DGL and tuned IMM/modi ed DGL in integrated estimation/guidance scheme with realistically modelled missile against various target maneuvers. Though the time taken to intercept is higher when a realistic model is considered, the integrated estimation/guidance law still performs better. The miss distance is observed to be similar to the one obtained by considering simpli ed kinematic models.